Do a round of cleanup

Also fix testing harness for task 1 and make tests for task 14 stronger

tutorials/ComplexArithmetic/Workbook_ComplexArithmetic.ipynb

@@ -98,7 +98,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "[Return to task 1 of the Complex Arithmetic kata.](./ComplexArithmetic.ipynb#Exercise-1:-Powers-of-$i$.)"
+    "[Return to task 1 of the Complex Arithmetic tutorial.](./ComplexArithmetic.ipynb#Exercise-1:-Powers-of-$i$.)"
    ]
   },
   {
@@ -156,7 +156,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "[Return to task 2 of the Complex Arithmetic kata.](./ComplexArithmetic.ipynb#Exercise-2:-Complex-addition.)"
+    "[Return to task 2 of the Complex Arithmetic tutorial.](./ComplexArithmetic.ipynb#Exercise-2:-Complex-addition.)"
    ]
   },
   {
@@ -209,7 +209,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "[Return to task 3 of the Complex Arithmetic kata.](./ComplexArithmetic.ipynb#Exercise-3:-Complex-multiplication.)"
+    "[Return to task 3 of the Complex Arithmetic tutorial.](./ComplexArithmetic.ipynb#Exercise-3:-Complex-multiplication.)"
    ]
   },
   {
@@ -256,7 +256,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "[Return to task 4 of the Complex Arithmetic kata.](./ComplexArithmetic.ipynb#Exercise-4:-Complex-conjugate.)"
+    "[Return to task 4 of the Complex Arithmetic tutorial.](./ComplexArithmetic.ipynb#Exercise-4:-Complex-conjugate.)"
    ]
   },
   {
@@ -317,7 +317,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "[Return to task 5 of the Complex Arithmetic kata.](./ComplexArithmetic.ipynb#Exercise-5:-Complex-division.)"
+    "[Return to task 5 of the Complex Arithmetic tutorial.](./ComplexArithmetic.ipynb#Exercise-5:-Complex-division.)"
    ]
   },
   {
@@ -367,7 +367,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "[Return to task 6 of the Complex Arithmetic kata.](./ComplexArithmetic.ipynb#Exercise-6:-Modulus.)"
+    "[Return to task 6 of the Complex Arithmetic tutorial.](./ComplexArithmetic.ipynb#Exercise-6:-Modulus.)"
    ]
   },
   {
@@ -419,7 +419,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "[Return to task 7 of the Complex Arithmetic kata.](./ComplexArithmetic.ipynb#Exercise-7:-Complex-exponents.)"
+    "[Return to task 7 of the Complex Arithmetic tutorial.](./ComplexArithmetic.ipynb#Exercise-7:-Complex-exponents.)"
    ]
   },
   {
@@ -493,7 +493,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "[Return to task 8 of the Complex Arithmetic kata.](./ComplexArithmetic.ipynb#Exercise-8*:-Complex-powers-of-real-numbers.)"
+    "[Return to task 8 of the Complex Arithmetic tutorial.](./ComplexArithmetic.ipynb#Exercise-8*:-Complex-powers-of-real-numbers.)"
    ]
   },
   {
@@ -563,7 +563,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "[Return to task 9 of the Complex Arithmetic kata.](./ComplexArithmetic.ipynb#Exercise-9:-Cartesian-to-polar-conversion.)"
+    "[Return to task 9 of the Complex Arithmetic tutorial.](./ComplexArithmetic.ipynb#Exercise-9:-Cartesian-to-polar-conversion.)"
    ]
   },
   {
@@ -609,7 +609,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "[Return to task 10 of the Complex Arithmetic kata.](./ComplexArithmetic.ipynb#Exercise-10:-Polar-to-Cartesian-conversion.)"
+    "[Return to task 10 of the Complex Arithmetic tutorial.](./ComplexArithmetic.ipynb#Exercise-10:-Polar-to-Cartesian-conversion.)"
    ]
   },
   {
@@ -686,7 +686,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "[Return to task 11 of the Complex Arithmetic kata.](./ComplexArithmetic.ipynb#Exercise-11:-Polar-multiplication.)"
+    "[Return to task 11 of the Complex Arithmetic tutorial.](./ComplexArithmetic.ipynb#Exercise-11:-Polar-multiplication.)"
    ]
   },
   {
@@ -754,7 +754,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "[Return to task 12 of the Complex Arithmetic kata.](./ComplexArithmetic.ipynb#Exercise-12**:-Arbitrary-complex-exponents.)"
+    "[Return to task 12 of the Complex Arithmetic tutorial.](./ComplexArithmetic.ipynb#Exercise-12**:-Arbitrary-complex-exponents.)"
    ]
   }
  ],

tutorials/LinearAlgebra/LinearAlgebra.ipynb

@@ -178,17 +178,17 @@
     "@exercise\n",
     "def matrix_add(a : Matrix, b : Matrix) -> Matrix:\n",
     "    # You can get the size of a matrix like this:\n",
-    "    n = len(a)\n",
-    "    m = len(a[0])\n",
+    "    rows = len(a)\n",
+    "    columns = len(a[0])\n",
     "    \n",
-    "    # You can use the following function to initialize an n×m matrix filled with 0s to store your answer\n",
-    "    c = create_empty_matrix(n, m)\n",
+    "    # You can use the following function to initialize a rows×columns matrix filled with 0s to store your answer\n",
+    "    c = create_empty_matrix(rows, columns)\n",
     "    \n",
     "    # You can use a for loop to execute its body several times;\n",
     "    # in this loop variable i will take on each value from 0 to n-1, inclusive\n",
-    "    for i in range(n):\n",
+    "    for i in range(rows):\n",
     "        # Loops can be nested\n",
-    "        for j in range(m):\n",
+    "        for j in range(columns):\n",
     "            # You can access elements of a matrix like this:\n",
     "            x = a[i][j]\n",
     "            y = b[i][j]\n",
@@ -766,8 +766,13 @@
     "    3 \\\\\n",
     "    -8\n",
     "\\end{bmatrix}\n",
-    "= (-6) \\cdot (3) + (-9i) \\cdot (-8) = -18 + 72i$$\n",
-    "\n",
+    "= (-6) \\cdot (3) + (-9i) \\cdot (-8) = -18 + 72i$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
     "If you are familiar with the **dot product**, you will notice that it is equivalent to inner product for real-numbered vectors.\n",
     "\n",
     "> We use our definition for these tutorials because it matches the notation used in quantum computing. You might encounter other sources which define the inner product a little differently: $\\langle V , W \\rangle = W^\\dagger V = V^T\\overline{W}$, in contrast to the $V^\\dagger W$ that we use. These definitions are almost equivalent, with some differences in the scalar multiplication by a complex number.\n",
@@ -1084,7 +1089,7 @@
     "<br/>\n",
     "<details>\n",
     "    <summary><strong>Need a hint? Click here</strong></summary>\n",
-    "    Multiply the matrix by the vector, then divide elements of the result by elements of the original vector. Don't forget though, some elements of the vector may be $0$.\n",
+    "    Multiply the matrix by the vector, then divide the elements of the result by the elements of the original vector. Don't forget though, some elements of the vector may be $0$.\n",
     "</details>"
    ]
   },