diff --git a/11_classes/00_content.ipynb b/11_classes/00_content.ipynb
index 692af9c..6852453 100644
--- a/11_classes/00_content.ipynb
+++ b/11_classes/00_content.ipynb
@@ -272,7 +272,7 @@
    "outputs": [],
    "source": [
     "class Vector:\n",
-    "    \"\"\"A standard one-dimensional vector from linear algebra.\"\"\"\n",
+    "    \"\"\"A one-dimensional vector from linear algebra.\"\"\"\n",
     "\n",
     "    dummy_variable = \"I am a vector\"\n",
     "\n",
@@ -403,7 +403,7 @@
      "data": {
       "text/plain": [
        "\u001b[0;31mInit signature:\u001b[0m \u001b[0mVector\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
-       "\u001b[0;31mDocstring:\u001b[0m      A standard one-dimensional vector from linear algebra.\n",
+       "\u001b[0;31mDocstring:\u001b[0m      A one-dimensional vector from linear algebra.\n",
        "\u001b[0;31mType:\u001b[0m           type\n",
        "\u001b[0;31mSubclasses:\u001b[0m     \n"
       ]
@@ -432,7 +432,7 @@
       "Help on class Vector in module __main__:\n",
       "\n",
       "class Vector(builtins.object)\n",
-      " |  A standard one-dimensional vector from linear algebra.\n",
+      " |  A one-dimensional vector from linear algebra.\n",
       " |  \n",
       " |  Methods defined here:\n",
       " |  \n",
@@ -484,7 +484,7 @@
      "data": {
       "text/plain": [
        "mappingproxy({'__module__': '__main__',\n",
-       "              '__doc__': 'A standard one-dimensional vector from linear algebra.',\n",
+       "              '__doc__': 'A one-dimensional vector from linear algebra.',\n",
        "              'dummy_variable': 'I am a vector',\n",
        "              'dummy_method': <function __main__.Vector.dummy_method(self)>,\n",
        "              '__dict__': <attribute '__dict__' of 'Vector' objects>,\n",
@@ -687,7 +687,7 @@
    "outputs": [],
    "source": [
     "class Vector:\n",
-    "    \"\"\"A standard one-dimensional vector from linear algebra.\n",
+    "    \"\"\"A one-dimensional vector from linear algebra.\n",
     "\n",
     "    All entries are converted to floats.\n",
     "    \"\"\"\n",
diff --git a/11_classes/02_content.ipynb b/11_classes/02_content.ipynb
index 1d99ecf..520339f 100644
--- a/11_classes/02_content.ipynb
+++ b/11_classes/02_content.ipynb
@@ -1815,17 +1815,16 @@
    },
    "outputs": [],
    "source": [
-    "def norm(vector_or_matrix):\n",
+    "def norm(vec_or_mat):\n",
     "    \"\"\"Calculate the Frobenius or Euclidean norm of a matrix or vector.\n",
     "\n",
     "    Args:\n",
-    "        vector_or_matrix (Vector/Matrix): the entries whose squares\n",
-    "            are summed up\n",
+    "        vec_or_mat (Vector / Matrix): object whose entries are squared and summed up\n",
     "\n",
     "    Returns:\n",
     "        norm (float)\n",
     "    \"\"\"\n",
-    "    return math.sqrt(sum(x ** 2 for x in vector_or_matrix))"
+    "    return math.sqrt(sum(x ** 2 for x in vec_or_mat))"
    ]
   },
   {
diff --git a/11_classes/03_content.ipynb b/11_classes/03_content.ipynb
index 7b3a9ae..9dc08a2 100644
--- a/11_classes/03_content.ipynb
+++ b/11_classes/03_content.ipynb
@@ -694,7 +694,7 @@
     "    def __add__(self, other):\n",
     "        if isinstance(other, self.__class__):  # vector addition\n",
     "            if len(self) != len(other):\n",
-    "                raise ValueError(\"vectors need to be of the same length\")\n",
+    "                raise ValueError(\"vectors must be of the same length\")\n",
     "            return Vector(x + y for (x, y) in zip(self, other))\n",
     "        elif isinstance(other, numbers.Number):  # broadcasting addition\n",
     "            return Vector(x + other for x in self)\n",
@@ -706,7 +706,7 @@
     "    def __sub__(self, other):\n",
     "        if isinstance(other, self.__class__):  # vector subtraction\n",
     "            if len(self) != len(other):\n",
-    "                raise ValueError(\"vectors need to be of the same length\")\n",
+    "                raise ValueError(\"vectors must be of the same length\")\n",
     "            return Vector(x - y for (x, y) in zip(self, other))\n",
     "        elif isinstance(other, numbers.Number):  # broadcasting subtraction\n",
     "            return Vector(x - other for x in self)\n",
@@ -721,7 +721,7 @@
     "    def __mul__(self, other):\n",
     "        if isinstance(other, self.__class__):  # dot product\n",
     "            if len(self) != len(other):\n",
-    "                raise ValueError(\"vectors need to be of the same length\")\n",
+    "                raise ValueError(\"vectors must be of the same length\")\n",
     "            return sum(x * y for (x, y) in zip(self, other))\n",
     "        elif isinstance(other, numbers.Number):  # scalar multiplication\n",
     "            return Vector(x * other for x in self)\n",
@@ -872,14 +872,14 @@
    "outputs": [
     {
      "ename": "ValueError",
-     "evalue": "vectors need to be of the same length",
+     "evalue": "vectors must be of the same length",
      "output_type": "error",
      "traceback": [
       "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
       "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
       "\u001b[0;32m<ipython-input-27-21fab2d5f12e>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mv\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mw\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
-      "\u001b[0;32m<ipython-input-21-12852bd26164>\u001b[0m in \u001b[0;36m__mul__\u001b[0;34m(self, other)\u001b[0m\n\u001b[1;32m     45\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0misinstance\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mother\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m__class__\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m  \u001b[0;31m# dot product\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     46\u001b[0m             \u001b[0;32mif\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m!=\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mother\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 47\u001b[0;31m                 \u001b[0;32mraise\u001b[0m \u001b[0mValueError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"vectors need to be of the same length\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     48\u001b[0m             \u001b[0;32mreturn\u001b[0m \u001b[0msum\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0my\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mzip\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mother\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     49\u001b[0m         \u001b[0;32melif\u001b[0m \u001b[0misinstance\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mother\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mnumbers\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mNumber\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m  \u001b[0;31m# scalar multiplication\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
-      "\u001b[0;31mValueError\u001b[0m: vectors need to be of the same length"
+      "\u001b[0;32m<ipython-input-21-e7b5dd8e219a>\u001b[0m in \u001b[0;36m__mul__\u001b[0;34m(self, other)\u001b[0m\n\u001b[1;32m     45\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0misinstance\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mother\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m__class__\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m  \u001b[0;31m# dot product\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     46\u001b[0m             \u001b[0;32mif\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m!=\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mother\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 47\u001b[0;31m                 \u001b[0;32mraise\u001b[0m \u001b[0mValueError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"vectors must be of the same length\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     48\u001b[0m             \u001b[0;32mreturn\u001b[0m \u001b[0msum\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0my\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mzip\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mother\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     49\u001b[0m         \u001b[0;32melif\u001b[0m \u001b[0misinstance\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mother\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mnumbers\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mNumber\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m  \u001b[0;31m# scalar multiplication\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;31mValueError\u001b[0m: vectors must be of the same length"
      ]
     }
    ],
@@ -992,14 +992,14 @@
    "outputs": [
     {
      "ename": "ValueError",
-     "evalue": "vectors need to be of the same length",
+     "evalue": "vectors must be of the same length",
      "output_type": "error",
      "traceback": [
       "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
       "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
       "\u001b[0;32m<ipython-input-31-490ee3f2b9e8>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mv\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mw\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
-      "\u001b[0;32m<ipython-input-21-12852bd26164>\u001b[0m in \u001b[0;36m__add__\u001b[0;34m(self, other)\u001b[0m\n\u001b[1;32m     18\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0misinstance\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mother\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m__class__\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m  \u001b[0;31m# vector addition\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     19\u001b[0m             \u001b[0;32mif\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m!=\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mother\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 20\u001b[0;31m                 \u001b[0;32mraise\u001b[0m \u001b[0mValueError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"vectors need to be of the same length\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     21\u001b[0m             \u001b[0;32mreturn\u001b[0m \u001b[0mVector\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0my\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mzip\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mother\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     22\u001b[0m         \u001b[0;32melif\u001b[0m \u001b[0misinstance\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mother\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mnumbers\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mNumber\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m  \u001b[0;31m# broadcasting addition\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
-      "\u001b[0;31mValueError\u001b[0m: vectors need to be of the same length"
+      "\u001b[0;32m<ipython-input-21-e7b5dd8e219a>\u001b[0m in \u001b[0;36m__add__\u001b[0;34m(self, other)\u001b[0m\n\u001b[1;32m     18\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0misinstance\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mother\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m__class__\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m  \u001b[0;31m# vector addition\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     19\u001b[0m             \u001b[0;32mif\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m!=\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mother\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 20\u001b[0;31m                 \u001b[0;32mraise\u001b[0m \u001b[0mValueError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"vectors must be of the same length\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     21\u001b[0m             \u001b[0;32mreturn\u001b[0m \u001b[0mVector\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0my\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mzip\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mother\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     22\u001b[0m         \u001b[0;32melif\u001b[0m \u001b[0misinstance\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mother\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mnumbers\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mNumber\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m  \u001b[0;31m# broadcasting addition\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;31mValueError\u001b[0m: vectors must be of the same length"
      ]
     }
    ],
@@ -1171,7 +1171,7 @@
     "    def __add__(self, other):\n",
     "        if isinstance(other, self.__class__):  # matrix addition\n",
     "            if (self.n_rows != other.n_rows) or (self.n_cols != other.n_cols):\n",
-    "                raise ValueError(\"matrices need to be of the same dimensions\")\n",
+    "                raise ValueError(\"matrices must have the same dimensions\")\n",
     "            return Matrix((s_col + o_col for (s_col, o_col) in zip(s_row, o_row))\n",
     "                          for (s_row, o_row) in zip(self._entries, other._entries))\n",
     "        elif isinstance(other, numbers.Number):  # broadcasting addition\n",
@@ -1186,7 +1186,7 @@
     "    def __sub__(self, other):\n",
     "        if isinstance(other, self.__class__):  # matrix subtraction\n",
     "            if (self.n_rows != other.n_rows) or (self.n_cols != other.n_cols):\n",
-    "                raise ValueError(\"matrices need to be of the same dimensions\")\n",
+    "                raise ValueError(\"matrices must have the same dimensions\")\n",
     "            return Matrix((s_col - o_col for (s_col, o_col) in zip(s_row, o_row))\n",
     "                          for (s_row, o_row) in zip(self._entries, other._entries))\n",
     "        elif isinstance(other, numbers.Number):  # broadcasting subtraction\n",
@@ -1203,7 +1203,7 @@
     "    \n",
     "    def _matrix_multiply(self, other):\n",
     "        if self.n_cols != other.n_rows:\n",
-    "            raise ValueError(\"matrices need to have compatible dimensions\")\n",
+    "            raise ValueError(\"matrices must have compatible dimensions\")\n",
     "        return Matrix((rv * cv for cv in other.cols()) for rv in self.rows())\n",
     "\n",
     "    def __mul__(self, other):\n",
@@ -1387,15 +1387,15 @@
    "outputs": [
     {
      "ename": "ValueError",
-     "evalue": "matrices need to have compatible dimensions",
+     "evalue": "matrices must have compatible dimensions",
      "output_type": "error",
      "traceback": [
       "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
       "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
       "\u001b[0;32m<ipython-input-41-b57a49d097c9>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mm\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mn\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
-      "\u001b[0;32m<ipython-input-35-f4e0bb37caf6>\u001b[0m in \u001b[0;36m__mul__\u001b[0;34m(self, other)\u001b[0m\n\u001b[1;32m     72\u001b[0m             \u001b[0;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_matrix_multiply\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mother\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mas_matrix\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mas_vector\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     73\u001b[0m         \u001b[0;32melif\u001b[0m \u001b[0misinstance\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mother\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m__class__\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 74\u001b[0;31m             \u001b[0;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_matrix_multiply\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mother\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     75\u001b[0m         \u001b[0;32mreturn\u001b[0m \u001b[0mNotImplemented\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     76\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
-      "\u001b[0;32m<ipython-input-35-f4e0bb37caf6>\u001b[0m in \u001b[0;36m_matrix_multiply\u001b[0;34m(self, other)\u001b[0m\n\u001b[1;32m     63\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0m_matrix_multiply\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mother\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     64\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mn_cols\u001b[0m \u001b[0;34m!=\u001b[0m \u001b[0mother\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mn_rows\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 65\u001b[0;31m             \u001b[0;32mraise\u001b[0m \u001b[0mValueError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"matrices need to have compatible dimensions\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     66\u001b[0m         \u001b[0;32mreturn\u001b[0m \u001b[0mMatrix\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mrv\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mcv\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mcv\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mother\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcols\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mrv\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrows\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     67\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
-      "\u001b[0;31mValueError\u001b[0m: matrices need to have compatible dimensions"
+      "\u001b[0;32m<ipython-input-35-def82d7b791b>\u001b[0m in \u001b[0;36m__mul__\u001b[0;34m(self, other)\u001b[0m\n\u001b[1;32m     72\u001b[0m             \u001b[0;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_matrix_multiply\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mother\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mas_matrix\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mas_vector\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     73\u001b[0m         \u001b[0;32melif\u001b[0m \u001b[0misinstance\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mother\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m__class__\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 74\u001b[0;31m             \u001b[0;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_matrix_multiply\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mother\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     75\u001b[0m         \u001b[0;32mreturn\u001b[0m \u001b[0mNotImplemented\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     76\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;32m<ipython-input-35-def82d7b791b>\u001b[0m in \u001b[0;36m_matrix_multiply\u001b[0;34m(self, other)\u001b[0m\n\u001b[1;32m     63\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0m_matrix_multiply\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mother\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     64\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mn_cols\u001b[0m \u001b[0;34m!=\u001b[0m \u001b[0mother\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mn_rows\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 65\u001b[0;31m             \u001b[0;32mraise\u001b[0m \u001b[0mValueError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"matrices must have compatible dimensions\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     66\u001b[0m         \u001b[0;32mreturn\u001b[0m \u001b[0mMatrix\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mrv\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mcv\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mcv\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mother\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcols\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mrv\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrows\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     67\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;31mValueError\u001b[0m: matrices must have compatible dimensions"
      ]
     }
    ],
@@ -1497,15 +1497,15 @@
    "outputs": [
     {
      "ename": "ValueError",
-     "evalue": "matrices need to have compatible dimensions",
+     "evalue": "matrices must have compatible dimensions",
      "output_type": "error",
      "traceback": [
       "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
       "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
       "\u001b[0;32m<ipython-input-45-9faf2ee0ae54>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mv\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mn\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
-      "\u001b[0;32m<ipython-input-35-f4e0bb37caf6>\u001b[0m in \u001b[0;36m__rmul__\u001b[0;34m(self, other)\u001b[0m\n\u001b[1;32m     79\u001b[0m             \u001b[0;32mreturn\u001b[0m \u001b[0mself\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mother\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     80\u001b[0m         \u001b[0;32melif\u001b[0m \u001b[0misinstance\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mother\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mVector\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 81\u001b[0;31m             \u001b[0;32mreturn\u001b[0m \u001b[0mother\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mas_matrix\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcolumn\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mFalse\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_matrix_multiply\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mas_vector\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     82\u001b[0m         \u001b[0;32mreturn\u001b[0m \u001b[0mNotImplemented\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     83\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
-      "\u001b[0;32m<ipython-input-35-f4e0bb37caf6>\u001b[0m in \u001b[0;36m_matrix_multiply\u001b[0;34m(self, other)\u001b[0m\n\u001b[1;32m     63\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0m_matrix_multiply\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mother\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     64\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mn_cols\u001b[0m \u001b[0;34m!=\u001b[0m \u001b[0mother\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mn_rows\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 65\u001b[0;31m             \u001b[0;32mraise\u001b[0m \u001b[0mValueError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"matrices need to have compatible dimensions\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     66\u001b[0m         \u001b[0;32mreturn\u001b[0m \u001b[0mMatrix\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mrv\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mcv\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mcv\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mother\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcols\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mrv\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrows\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     67\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
-      "\u001b[0;31mValueError\u001b[0m: matrices need to have compatible dimensions"
+      "\u001b[0;32m<ipython-input-35-def82d7b791b>\u001b[0m in \u001b[0;36m__rmul__\u001b[0;34m(self, other)\u001b[0m\n\u001b[1;32m     79\u001b[0m             \u001b[0;32mreturn\u001b[0m \u001b[0mself\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mother\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     80\u001b[0m         \u001b[0;32melif\u001b[0m \u001b[0misinstance\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mother\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mVector\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 81\u001b[0;31m             \u001b[0;32mreturn\u001b[0m \u001b[0mother\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mas_matrix\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcolumn\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mFalse\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_matrix_multiply\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mas_vector\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     82\u001b[0m         \u001b[0;32mreturn\u001b[0m \u001b[0mNotImplemented\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     83\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;32m<ipython-input-35-def82d7b791b>\u001b[0m in \u001b[0;36m_matrix_multiply\u001b[0;34m(self, other)\u001b[0m\n\u001b[1;32m     63\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0m_matrix_multiply\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mother\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     64\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mn_cols\u001b[0m \u001b[0;34m!=\u001b[0m \u001b[0mother\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mn_rows\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 65\u001b[0;31m             \u001b[0;32mraise\u001b[0m \u001b[0mValueError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"matrices must have compatible dimensions\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     66\u001b[0m         \u001b[0;32mreturn\u001b[0m \u001b[0mMatrix\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mrv\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mcv\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mcv\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mother\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcols\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mrv\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrows\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     67\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;31mValueError\u001b[0m: matrices must have compatible dimensions"
      ]
     }
    ],
@@ -1736,7 +1736,7 @@
     "    def __eq__(self, other):\n",
     "        if isinstance(other, self.__class__):\n",
     "            if len(self) != len(other):\n",
-    "                raise ValueError(\"vectors need to be of the same length\")\n",
+    "                raise ValueError(\"vectors must be of the same length\")\n",
     "            for x, y in zip(self, other):\n",
     "                if abs(x - y) > self.zero_threshold:\n",
     "                    return False  # exit early if two corresponding entries differ\n",
@@ -1972,12 +1972,9 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "def norm(vector_or_matrix):\n",
-    "    \"\"\"Calculate the Frobenius or Euclidean norm of a matrix or vector.\n",
-    "    \n",
-    "    ...\n",
-    "    \"\"\"\n",
-    "    return math.sqrt(sum(x ** 2 for x in vector_or_matrix))"
+    "def norm(vec_or_mat):\n",
+    "    \"\"\"Calculate the Frobenius or Euclidean norm of a matrix or vector.\"\"\"\n",
+    "    return math.sqrt(sum(x ** 2 for x in vec_or_mat))"
    ]
   },
   {
@@ -2020,7 +2017,7 @@
     "\n",
     "    def __float__(self):\n",
     "        if len(self) != 1:\n",
-    "            raise RuntimeError(\"vector must have one entry to become a scalar\")\n",
+    "            raise RuntimeError(\"vector must have exactly one entry to become a scalar\")\n",
     "        return self._entries[0]"
    ]
   },
@@ -2303,14 +2300,14 @@
    "outputs": [
     {
      "ename": "RuntimeError",
-     "evalue": "vector must have one entry to become a scalar",
+     "evalue": "vector must have exactly one entry to become a scalar",
      "output_type": "error",
      "traceback": [
       "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
       "\u001b[0;31mRuntimeError\u001b[0m                              Traceback (most recent call last)",
       "\u001b[0;32m<ipython-input-75-8369cec552f3>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mfloat\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mv\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
-      "\u001b[0;32m<ipython-input-63-01438fec4aa0>\u001b[0m in \u001b[0;36m__float__\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m     29\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0m__float__\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     30\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m!=\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 31\u001b[0;31m             \u001b[0;32mraise\u001b[0m \u001b[0mRuntimeError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"vector must have one entry to become a scalar\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     32\u001b[0m         \u001b[0;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_entries\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
-      "\u001b[0;31mRuntimeError\u001b[0m: vector must have one entry to become a scalar"
+      "\u001b[0;32m<ipython-input-63-67b90fc89e7c>\u001b[0m in \u001b[0;36m__float__\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m     29\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0m__float__\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     30\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m!=\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 31\u001b[0;31m             \u001b[0;32mraise\u001b[0m \u001b[0mRuntimeError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"vector must have exactly one entry to become a scalar\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     32\u001b[0m         \u001b[0;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_entries\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;31mRuntimeError\u001b[0m: vector must have exactly one entry to become a scalar"
      ]
     }
    ],
diff --git a/11_classes/sample_package/__init__.py b/11_classes/sample_package/__init__.py
new file mode 100644
index 0000000..1e8d12c
--- /dev/null
+++ b/11_classes/sample_package/__init__.py
@@ -0,0 +1,30 @@
+"""This package provides linear algebra functionalities.
+
+The package is split into three modules:
+- matrix: defines the Matrix class
+- vector: defines the Vector class
+- utils: defines the norm() function that is shared by Matrix and Vector
+         and package-wide constants
+
+The classes implement arithmetic operations involving vectors and matrices.
+
+See the docstrings in the modules and classes for further info.
+"""
+
+# Import the classes here so that they are available
+# from the package's top level. That means that a user
+# who imports this package with `import sample_package`
+# may then refer to, for example, the Matrix class with
+# simply `sample_package.Matrix` instead of the longer
+# `sample_package.matrix.Matrix`.
+from sample_package.matrix import Matrix
+from sample_package.vector import Vector
+
+
+# Define meta information for the package.
+# There are other (and more modern) ways of
+# doing this, but specifying the following
+# dunder variables here is the traditional way.
+__name__ = "linear_algebra_tools"
+__version__ = "0.1.0"  # see https://semver.org/ for how the format works
+__author__ = "Alexander Hess"
diff --git a/11_classes/sample_package/matrix.py b/11_classes/sample_package/matrix.py
new file mode 100644
index 0000000..b64e50d
--- /dev/null
+++ b/11_classes/sample_package/matrix.py
@@ -0,0 +1,416 @@
+"""This module defines a Matrix class."""
+
+import numbers
+
+# Note the import at the bottom of this file, and
+# see the comments about imports in the matrix module.
+from sample_package import utils
+
+
+class Matrix:
+    """An m-by-n-dimensional matrix from linear algebra.
+
+    All entries are converted to floats, or whatever is set in the typing attribute.
+
+    Attributes:
+        storage (callable): data type used to store the entries internally;
+            defaults to tuple
+        typing (callable): type casting applied to all entries upon creation;
+            defaults to float
+        zero_threshold (float): max. tolerance when comparing an entry to zero;
+            defaults to 1e-12
+    """
+
+    storage = utils.DEFAULT_ENTRIES_STORAGE
+    typing = utils.DEFAULT_ENTRY_TYPE
+    zero_threshold = utils.ZERO_THRESHOLD
+
+    def __init__(self, data):
+        """Create a new matrix.
+
+        Args:
+            data (sequence of sequences): the matrix's entries;
+                viewed as a sequence of the matrix's rows (i.e., row-major order);
+                use the .from_columns() class method if the data come as a sequence
+                of the matrix's columns (i.e., column-major order)
+
+        Raises:
+            ValueError:
+                - if no entries are provided
+                - if the number of columns is inconsistent across the rows
+        """
+        self._entries = self.storage(
+            self.storage(self.typing(x) for x in r) for r in data
+        )
+        for row in self._entries[1:]:
+            if len(row) != self.n_cols:
+                raise ValueError("rows must have the same number of entries")
+        if len(self) == 0:
+            raise ValueError("a matrix must have at least one entry")
+
+    @classmethod
+    def from_columns(cls, data):
+        """Create a new matrix.
+
+        This is an alternative constructor for data provided in column-major order.
+
+        Args:
+            data (sequence of sequences): the matrix's entries;
+                viewed as a sequence of the matrix's columns (i.e., column-major order);
+                use the normal constructor method if the data come as a sequence
+                of the matrix's rows (i.e., row-major order)
+
+        Raises:
+            ValueError:
+                - if no entries are provided
+                - if the number of rows is inconsistent across the columns
+        """
+        return cls(data).transpose()
+
+    @classmethod
+    def from_rows(cls, data):
+        """See docstring for .__init__()."""
+        # Some users may want to use this .from_rows() constructor
+        # to explicitly communicate that the data are in row-major order.
+        # Otherwise, this method is redundant.
+        return cls(data)
+
+    def __repr__(self):
+        """Text representation of a Matrix."""
+        name = self.__class__.__name__
+        args = ", ".join(
+            "(" + ", ".join(f"{c:.3f}" for c in r) + ",)" for r in self._entries
+        )
+        return f"{name}(({args}))"
+
+    def __str__(self):
+        """Human-readable text representation of a Matrix."""
+        name = self.__class__.__name__
+        first, last, m, n = self[0], self[-1], self.n_rows, self.n_cols
+        return f"{name}(({first:.1f}, ...), ..., (..., {last:.1f}))[{m:d}x{n:d}]"
+
+    @property
+    def n_rows(self):
+        """Number of rows in a Matrix."""
+        return len(self._entries)
+
+    @property
+    def n_cols(self):
+        """Number of columns in a Matrix."""
+        return len(self._entries[0])
+
+    def __len__(self):
+        """Number of entries in a Matrix."""
+        return self.n_rows * self.n_cols
+
+    def __getitem__(self, index):
+        """Obtain an individual entry of a Matrix.
+
+        Args:
+            index (int / tuple of int's): if index is an integer,
+                the Matrix is viewed as a sequence in row-major order;
+                if index is a tuple of integers, the first one refers to
+                the row and the second one to the column of the entry
+
+        Returns:
+            entry (Matrix.typing)
+
+        Example Usage:
+            >>> m = Matrix([(1, 2), (3, 4)])
+            >>> m[0]
+            1.0
+            >>> m[-1]
+            4.0
+            >>> m[0, 1]
+            3.0
+        """
+        # Sequence-like indexing (one-dimensional)
+        if isinstance(index, int):
+            if index < 0:
+                index += len(self)
+            if not (0 <= index < len(self)):
+                raise IndexError("integer index out of range")
+            row, col = divmod(index, self.n_cols)
+            return self._entries[row][col]
+        # Mathematical-like indexing (two-dimensional)
+        elif (
+            isinstance(index, tuple)
+            and len(index) == 2
+            and isinstance(index[0], int)
+            and isinstance(index[1], int)
+        ):
+            return self._entries[index[0]][index[1]]
+        raise TypeError("index must be either an int or a tuple of two int's")
+
+    def rows(self):
+        """Loop over a Matrix's rows.
+
+        Returns:
+            rows (generator): produces a Matrix's rows as Vectors
+        """
+        return (Vector(r) for r in self._entries)
+
+    def cols(self):
+        """Loop over a Matrix's columns.
+
+        Returns:
+            columns (generator): produces a Matrix's columns as Vectors
+        """
+        return (
+            Vector(self._entries[r][c] for r in range(self.n_rows))
+            for c in range(self.n_cols)
+        )
+
+    def entries(self, *, reverse=False, row_major=True):
+        """Loop over a Matrix's entries.
+
+        Args:
+            reverse (bool): flag to loop backwards; defaults to False
+            row_major (bool): flag to loop in row-major order; defaults to True
+
+        Returns:
+            entries (generator): produces a Matrix's entries
+        """
+        if reverse:
+            rows = range(self.n_rows - 1, -1, -1)
+            cols = range(self.n_cols - 1, -1, -1)
+        else:
+            rows, cols = range(self.n_rows), range(self.n_cols)
+        if row_major:
+            return (self._entries[r][c] for r in rows for c in cols)
+        return (self._entries[r][c] for c in cols for r in rows)
+
+    def __iter__(self):
+        """Loop over a Matrix's entries.
+
+        See .entries() for more customization options.
+        """
+        return self.entries()
+
+    def __reversed__(self):
+        """Loop over a Matrix's entries in reverse order.
+
+        See .entries() for more customization options.
+        """
+        return self.entries(reverse=True)
+
+    def __add__(self, other):
+        """Handle `self + other` and `other + self`.
+
+        This may be either matrix addition or broadcasting addition.
+
+        Example Usage:
+            >>> Matrix([(1, 2), (3, 4)]) + Matrix([(2, 3), (4, 5)])
+            Matrix(((3.0, 5.0), (7.0, 9.0)))
+
+            >>> Matrix([(1, 2), (3, 4)]) + 5
+            Matrix(((6.0, 7.0), (8.0, 9.0)))
+
+            >>> 10 + Matrix([(1, 2), (3, 4)])
+            Matrix(((11.0, 12.0), (13.0, 14.0)))
+        """
+        # Matrix addition
+        if isinstance(other, self.__class__):
+            if (self.n_rows != other.n_rows) or (self.n_cols != other.n_cols):
+                raise ValueError("matrices must have the same dimensions")
+            return self.__class__(
+                (s_col + o_col for (s_col, o_col) in zip(s_row, o_row))
+                for (s_row, o_row) in zip(self._entries, other._entries)
+            )
+        # Broadcasting addition
+        elif isinstance(other, numbers.Number):
+            return self.__class__((c + other for c in r) for r in self._entries)
+        return NotImplemented
+
+    def __radd__(self, other):
+        """See docstring for .__add__()."""
+        if isinstance(other, Vector):
+            raise TypeError("vectors and matrices cannot be added")
+        # As both matrix and broadcasting addition are commutative,
+        # we dispatch to .__add__().
+        return self + other
+
+    def __sub__(self, other):
+        """Handle `self - other` and `other - self`.
+
+        This may be either matrix subtraction or broadcasting subtraction.
+
+        Example Usage:
+            >>> Matrix([(2, 3), (4, 5)]) - Matrix([(1, 2), (3, 4)])
+            Matrix(((1.0, 1.0), (1.0, 1.0)))
+
+            >>> Matrix([(1, 2), (3, 4)]) - 1
+            Matrix(((0.0, 1.0), (2.0, 3.0)))
+
+            >>> 10 - Matrix([(1, 2), (3, 4)])
+            Matrix(((9.0, 8.0), (7.0, 6.0)))
+        """
+        # As subtraction is the inverse of addition,
+        # we first dispatch to .__neg__() to invert the signs of
+        # all entries in other and then dispatch to .__add__().
+        return self + (-other)
+
+    def __rsub__(self, other):
+        """See docstring for .__sub__()."""
+        if isinstance(other, Vector):
+            raise TypeError("vectors and matrices cannot be subtracted")
+        # Same comments as in .__sub__() apply
+        # with the roles of self and other swapped.
+        return (-self) + other
+
+    def _matrix_multiply(self, other):
+        """Internal utility method to multiply to Matrix instances."""
+        if self.n_cols != other.n_rows:
+            raise ValueError("matrices must have compatible dimensions")
+        # Matrix-matrix multiplication means that each entry of the resulting
+        # Matrix is the dot product of the respective row of the "left" Matrix
+        # and column of the "right" Matrix. So, the rows/columns are represented
+        # by the Vector instances provided by the .cols() and .rows() methods.
+        return self.__class__((rv * cv for cv in other.cols()) for rv in self.rows())
+
+    def __mul__(self, other):
+        """Handle `self * other` and `other * self`.
+
+        This may be either scalar multiplication, matrix-vector multiplication,
+        vector-matrix multiplication, or matrix-matrix multiplication.
+
+        Example Usage:
+            >>> Matrix([(1, 2), (3, 4)]) * Matrix([(1, 2), (3, 4)])
+            Matrix(((7.0, 10.0), (15.0, 22.0)))
+
+            >>> 2 * Matrix([(1, 2), (3, 4)])
+            Matrix(((2.0, 4.0), (6.0, 8.0)))
+
+            >>> Matrix([(1, 2), (3, 4)]) * 3
+            Matrix(((3.0, 6.0), (9.0, 12.0)))
+
+            Matrix-vector and vector-matrix multiplication are not commutative.
+
+            >>> Matrix([(1, 2), (3, 4)]) * Vector([5, 6])
+            Vector((17.0, 39.0))
+
+            >>> Vector([5, 6]) * Matrix([(1, 2), (3, 4)])
+            Vector((23.0, 34.0))
+        """
+        # Scalar multiplication
+        if isinstance(other, numbers.Number):
+            return self.__class__((x * other for x in r) for r in self._entries)
+        # Matrix-vector multiplication: Vector is a column Vector
+        elif isinstance(other, Vector):
+            # First, cast the other Vector as a Matrix, then do matrix-matrix
+            # multiplication, and lastly return the result as a Vector again.
+            return self._matrix_multiply(other.as_matrix()).as_vector()
+        # Matrix-matrix multiplication
+        elif isinstance(other, self.__class__):
+            return self._matrix_multiply(other)
+        return NotImplemented
+
+    def __rmul__(self, other):
+        """See docstring for .__mul__()."""
+        # As scalar multiplication is commutative, we dispatch to .__mul__().
+        if isinstance(other, numbers.Number):
+            return self * other
+        # Vector-matrix multiplication: Vector is a row Vector
+        elif isinstance(other, Vector):
+            return other.as_matrix(column=False)._matrix_multiply(self).as_vector()
+        return NotImplemented
+
+    def __truediv__(self, other):
+        """Handle `self / other`.
+
+        Divide a Matrix by a scalar.
+
+        Example Usage:
+            >>> Matrix([(1, 2), (3, 4)]) / 4
+            Matrix([(0.25, 0.5), (0.75, 1.0)])
+        """
+        # As scalar division division is the same as multiplication
+        # with the inverse, we dispatch to .__mul__().
+        if isinstance(other, numbers.Number):
+            return self * (1 / other)
+        return NotImplemented
+
+    def __eq__(self, other):
+        """Handle `self == other`.
+
+        Compare two Matrix instances for equality.
+
+        Example Usage:
+            >>> Matrix([(1, 2), (3, 4)]) == Matrix([(1, 2), (3, 4)])
+            True
+
+            >>> Matrix([(1, 2), (3, 4)]) == Matrix([(5, 6), (7, 8)])
+            False
+        """
+        if isinstance(other, self.__class__):
+            if (self.n_rows != other.n_rows) or (self.n_cols != other.n_cols):
+                raise ValueError("matrices must have the same dimensions")
+            for x, y in zip(self, other):
+                if abs(x - y) > self.zero_threshold:
+                    return False  # exit early if two corresponding entries differ
+            return True
+        return NotImplemented
+
+    def __pos__(self):
+        """Handle `+self`.
+
+        This is simply an identity operator returning the Matrix itself.
+        """
+        return self
+
+    def __neg__(self):
+        """Handle `-self`.
+
+        Negate all entries of a Matrix.
+        """
+        return self.__class__((-x for x in r) for r in self._entries)
+
+    def __abs__(self):
+        """The Frobenius norm of a Matrix."""
+        return utils.norm(self)  # use the norm() function shared with the Vector class
+
+    def __bool__(self):
+        """A Matrix is truthy if its Frobenius norm is strictly positive."""
+        return bool(abs(self))
+
+    def __float__(self):
+        """Cast a Matrix as a scalar.
+
+        Returns:
+            scalar (float)
+
+        Raises:
+            RuntimeError: if the Matrix has more than one entry
+        """
+        if not (self.n_rows == 1 and self.n_cols == 1):
+            raise RuntimeError("matrix must have exactly one entry to become a scalar")
+        return self[0]
+
+    def as_vector(self):
+        """Get a Vector representation of a Matrix.
+
+        Returns:
+            vector (Vector)
+
+        Raises:
+            RuntimeError: if one of the two dimensions, .n_rows or .n_cols, is not 1
+        """
+        if not (self.n_rows == 1 or self.n_cols == 1):
+            raise RuntimeError("one dimension (m or n) must be 1")
+        return Vector(x for x in self)
+
+    def transpose(self):
+        """Switch the rows and columns of a Matrix.
+
+        Returns:
+            matrix (Matrix)
+        """
+        return self.__class__(zip(*self._entries))
+
+
+# This import needs to be made here as otherwise an ImportError is raised.
+# That is so as both the matrix and vector modules import a class from each other.
+# We call that a circular import. Whereas Python handles "circular" references
+# (e.g., both the Matrix and Vector classes have methods that reference the
+# respective other class), that is forbidden for imports.
+from sample_package.vector import Vector
diff --git a/11_classes/sample_package/utils.py b/11_classes/sample_package/utils.py
new file mode 100644
index 0000000..2720372
--- /dev/null
+++ b/11_classes/sample_package/utils.py
@@ -0,0 +1,35 @@
+"""This module provides utilities for the whole package.
+
+The defined constants are used as defaults in the Vector and Matrix classes.
+
+The norm() function is shared by Vector.__abs__() and Matrix.__abs__().
+"""
+
+import math
+
+
+# Define constants (i.e., normal variables that are, by convention, named in UPPERCASE)
+# that are used as the defaults for class attributes within Vector and Matrix.
+DEFAULT_ENTRIES_STORAGE = tuple
+DEFAULT_ENTRY_TYPE = float
+ZERO_THRESHOLD = 1e-12
+
+
+def norm(vec_or_mat):
+    """Calculate the Frobenius or Euclidean norm of a matrix or vector.
+
+    Find more infos here: https://en.wikipedia.org/wiki/Matrix_norm#Frobenius_norm
+
+    Args:
+        vec_or_mat (Vector / Matrix): object whose entries are squared and summed up
+
+    Returns:
+        norm (float)
+
+    Example Usage:
+        As Vector and Matrix objects are by design non-empty sequences,
+        norm() may be called, for example, with `[3, 4]` as the argument:
+        >>> norm([3, 4])
+        5.0
+    """
+    return math.sqrt(sum(x ** 2 for x in vec_or_mat))
diff --git a/11_classes/sample_package/vector.py b/11_classes/sample_package/vector.py
new file mode 100644
index 0000000..1b6e305
--- /dev/null
+++ b/11_classes/sample_package/vector.py
@@ -0,0 +1,253 @@
+"""This module defines a Vector class."""
+
+# Imports from the standard library go first ...
+import numbers
+
+# ... and are followed by project-internal ones.
+# If third-party libraries are needed, they are
+# put into a group on their own in between.
+# Within a group, imports are sorted lexicographically.
+from sample_package import utils
+from sample_package.matrix import Matrix
+
+
+class Vector:
+    """A one-dimensional vector from linear algebra.
+
+    All entries are converted to floats, or whatever is set in the typing attribute.
+
+    Attributes:
+        storage (callable): data type used to store the entries internally;
+            defaults to tuple
+        typing (callable): type casting applied to all entries upon creation;
+            defaults to float
+        zero_threshold (float): max. tolerance when comparing an entry to zero;
+            defaults to 1e-12
+    """
+
+    storage = utils.DEFAULT_ENTRIES_STORAGE
+    typing = utils.DEFAULT_ENTRY_TYPE
+    zero_threshold = utils.ZERO_THRESHOLD
+
+    def __init__(self, data):
+        """Create a new vector.
+
+        Args:
+            data (sequence): the vector's entries
+
+        Raises:
+            ValueError: if no entries are provided
+
+        Example Usage:
+            >>> Vector([1, 2, 3])
+            Vector((1.0, 2.0, 3.0))
+
+            >>> Vector(range(3))
+            Vector((0.0, 1.0, 2.0))
+        """
+        self._entries = self.storage(self.typing(x) for x in data)
+        if len(self) == 0:
+            raise ValueError("a vector must have at least one entry")
+
+    def __repr__(self):
+        """Text representation of a Vector."""
+        name = self.__class__.__name__
+        args = ", ".join(f"{x:.3f}" for x in self)
+        return f"{name}(({args}))"
+
+    def __str__(self):
+        """Human-readable text representation of a Vector."""
+        name = self.__class__.__name__
+        first, last, n_entries = self[0], self[-1], len(self)
+        return f"{name}({first:.1f}, ..., {last:.1f})[{n_entries:d}]"
+
+    def __len__(self):
+        """Number of entries in a Vector."""
+        return len(self._entries)
+
+    def __getitem__(self, index):
+        """Obtain an individual entry of a Vector."""
+        if not isinstance(index, int):
+            raise TypeError("index must be an integer")
+        return self._entries[index]
+
+    def __iter__(self):
+        """Loop over a Vector's entries."""
+        return iter(self._entries)
+
+    def __reversed__(self):
+        """Loop over a Vector's entries in reverse order."""
+        return reversed(self._entries)
+
+    def __add__(self, other):
+        """Handle `self + other` and `other + self`.
+
+        This may be either vector addition or broadcasting addition.
+
+        Example Usage:
+            >>> Vector([1, 2, 3]) + Vector([2, 3, 4])
+            Vector((3, 5, 7))
+
+            >>> Vector([1, 2, 3]) + 4
+            Vector((5, 6, 7))
+
+            >>> 10 + Vector([1, 2, 3])
+            Vector((11, 12, 13))
+        """
+        # Vector addition
+        if isinstance(other, self.__class__):
+            if len(self) != len(other):
+                raise ValueError("vectors must be of the same length")
+            return self.__class__(x + y for (x, y) in zip(self, other))
+        # Broadcasting addition
+        elif isinstance(other, numbers.Number):
+            return self.__class__(x + other for x in self)
+        return NotImplemented
+
+    def __radd__(self, other):
+        """See docstring for .__add__()."""
+        # As both vector and broadcasting addition are commutative,
+        # we dispatch to .__add__().
+        return self + other
+
+    def __sub__(self, other):
+        """Handle `self - other` and `other - self`.
+
+        This may be either vector subtraction or broadcasting subtraction.
+
+        Example Usage:
+            >>> Vector([7, 8, 9]) - Vector([1, 2, 3])
+            Vector((6, 6, 6))
+
+            >>> Vector([1, 2, 3]) - 1
+            Vector((0, 1, 2))
+
+            >>> 10 - Vector([1, 2, 3])
+            Vector((9, 8, 7))
+        """
+        # As subtraction is the inverse of addition,
+        # we first dispatch to .__neg__() to invert the signs of
+        # all entries in other and then dispatch to .__add__().
+        return self + (-other)
+
+    def __rsub__(self, other):
+        """See docstring for .__sub__()."""
+        # Same comments as in .__sub__() apply
+        # with the roles of self and other swapped.
+        return (-self) + other
+
+    def __mul__(self, other):
+        """Handle `self * other` and `other * self`.
+
+        This may be either the dot product of two vectors or scalar multiplication.
+
+        Example Usage:
+            >>> Vector([1, 2, 3]) * Vector([2, 3, 4])
+            14
+
+            >>> 2 * Vector([1, 2, 3])
+            Vector((2.0, 4.0, 6.0))
+
+            >>> Vector([1, 2, 3]) * 3
+            Vector((3.0, 6.0, 9.0))
+        """
+        # Dot product
+        if isinstance(other, self.__class__):
+            if len(self) != len(other):
+                raise ValueError("vectors must be of the same length")
+            return sum(x * y for (x, y) in zip(self, other))
+        # Scalar multiplication
+        elif isinstance(other, numbers.Number):
+            return self.__class__(x * other for x in self)
+        return NotImplemented
+
+    def __rmul__(self, other):
+        """See docstring for .__mul__()."""
+        # As both dot product and scalar multiplication are commutative,
+        # we dispatch to .__mul__().
+        return self * other
+
+    def __truediv__(self, other):
+        """Handle `self / other`.
+
+        Divide a Vector by a scalar.
+
+        Example Usage:
+            >>> Vector([9, 6, 12]) / 3
+            Vector((3.0, 2.0, 4.0))
+        """
+        # As scalar division division is the same as multiplication
+        # with the inverse, we dispatch to .__mul__().
+        if isinstance(other, numbers.Number):
+            return self * (1 / other)
+        return NotImplemented
+
+    def __eq__(self, other):
+        """Handle `self == other`.
+
+        Compare two Vectors for equality.
+
+        Example Usage:
+            >>> Vector([1, 2, 3]) == Vector([1, 2, 3])
+            True
+
+            >>> Vector([1, 2, 3]) == Vector([4, 5, 6])
+            False
+        """
+        if isinstance(other, self.__class__):
+            if len(self) != len(other):
+                raise ValueError("vectors must be of the same length")
+            for x, y in zip(self, other):
+                if abs(x - y) > self.zero_threshold:
+                    return False  # exit early if two corresponding entries differ
+            return True
+        return NotImplemented
+
+    def __pos__(self):
+        """Handle `+self`.
+
+        This is simply an identity operator returning the Vector itself.
+        """
+        return self
+
+    def __neg__(self):
+        """Handle `-self`.
+
+        Negate all entries of a Vector.
+        """
+        return self.__class__(-x for x in self)
+
+    def __abs__(self):
+        """The Euclidean norm of a vector."""
+        return utils.norm(self)  # use the norm() function shared with the Matrix class
+
+    def __bool__(self):
+        """A Vector is truthy if its Euclidean norm is strictly positive."""
+        return bool(abs(self))
+
+    def __float__(self):
+        """Cast a Vector as a scalar.
+
+        Returns:
+            scalar (float)
+
+        Raises:
+            RuntimeError: if the Vector has more than one entry
+        """
+        if len(self) != 1:
+            raise RuntimeError("vector must have exactly one entry to become a scalar")
+        return self[0]
+
+    def as_matrix(self, *, column=True):
+        """Get a Matrix representation of a Vector.
+
+        Args:
+            column (bool): if the vector is interpreted as a
+                column vector or a row vector; defaults to True
+
+        Returns:
+            matrix (Matrix)
+        """
+        if column:
+            return Matrix([x] for x in self)
+        return Matrix([(x for x in self)])