Spell checked

StephenElston · StephenElston · commit db6179235321 · 2018-07-08T20:26:08.000-07:00
diff --git a/Module03/03-01-Vectors.ipynb b/Module03/03-01-Vectors.ipynb
@@ -15,7 +15,7 @@
     "Our vector can be written as **v**=(2,1), but more formally we would use the following notation, in which the dimensional coordinate values for the vector are shown as a matrix:\n",
     "\\begin{equation}\\vec{v} = \\begin{bmatrix}2 \\\\ 1 \\end{bmatrix}\\end{equation}\n",
     "\n",
-    "So what exactly does that mean? Well, the coordinate is two-dimensional, and describes the movements required to get to the end point (of *head*) of the vector - in this case, we need to move 2 units in the *x* dimension, and 1 unit in the *y* dimension. Note that we don't specify a starting point for the vector - we're simply describing a destination coordinate that encapsulate the magnitide and direction of the vector. Think about it as the directions you need to follow to get to *there* from *here*, without specifying where *here* actually is!\n",
+    "So what exactly does that mean? Well, the coordinate is two-dimensional, and describes the movements required to get to the end point (of *head*) of the vector - in this case, we need to move 2 units in the *x* dimension, and 1 unit in the *y* dimension. Note that we don't specify a starting point for the vector - we're simply describing a destination coordinate that encapsulate the magnitude and direction of the vector. Think about it as the directions you need to follow to get to *there* from *here*, without specifying where *here* actually is!\n",
     "\n",
     "It can help to visualize the vector, and with a two-dimensional vector, that's pretty straightforward. We just define a two-dimensional plane, choose a starting point, and plot the coordinate described by the vector relative to the starting point.\n",
     "\n",
@@ -63,12 +63,12 @@
    "metadata": {},
    "source": [
     "## Calculating Vector Magnitude and Direction\n",
-    "We tend to work with vectors by expressing their components as *cartesian coordinates*; that is, *x* and *y* (and other dimension) values that define the number of units travelled along each dimension. So the coordinates of our (2,1) vector indicate that we must travel 2 units along the *x* axis, and *1* unit along the *y* axis.\n",
+    "We tend to work with vectors by expressing their components as *cartesian coordinates*; that is, *x* and *y* (and other dimension) values that define the number of units traveled along each dimension. So the coordinates of our (2,1) vector indicate that we must travel 2 units along the *x* axis, and *1* unit along the *y* axis.\n",
     "\n",
-    "However, you can also work with verctors in terms of their *polar coordinates*; that is coordinates that describe the magnitude and direction of the vector. The magnitude is the overall distance of the vector from tail to head, and the direction is the angle at which the vector is oriented.\n",
+    "However, you can also work with vectors in terms of their *polar coordinates*; that is coordinates that describe the magnitude and direction of the vector. The magnitude is the overall distance of the vector from tail to head, and the direction is the angle at which the vector is oriented.\n",
     "\n",
     "### Calculating Magnitude\n",
-    "Calculating the magnitude of the vector from its cartesian coordinates requires measuring the distance between the arbitrary starting point and the vector head point. For a two-dimensional vector, we're actually just calculating the length of the hypotenuse in a right-angled triangle - so we could simply invoke Pythagorean theorum and calculate the square root of the sum of the squares of it's components, like this:\n",
+    "Calculating the magnitude of the vector from its cartesian coordinates requires measuring the distance between the arbitrary starting point and the vector head point. For a two-dimensional vector, we're actually just calculating the length of the hypotenuse in a right-angled triangle - so we could simply invoke Pythagorean theorem and calculate the square root of the sum of the squares of it's components, like this:\n",
     "\n",
     "\\begin{equation}\\|\\vec{v}\\| = \\sqrt{v_{1}\\;^{2} + v_{2}\\;^{2}}\\end{equation}\n",
     "\n",
@@ -387,6 +387,13 @@
     "\n",
     "Note on the plot that if you simply moved the tail of the blue arrow so that it started at the head of red arrow, its head would end up in the same place as the head of the green arrow; and the same would be true if you moved tail of the red arrow to the head of the blue arrow."
    ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
   }
  ],
  "metadata": {
diff --git a/Module03/03-05-Transformations Eigenvectors and Eigenvalues.ipynb b/Module03/03-05-Transformations Eigenvectors and Eigenvalues.ipynb
@@ -1081,7 +1081,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "In cases like these, where a matrix transformation is the equivelent of a scalar-vector multiplication, the scalar-vector pairs that correspond to the matrix are known respectively as eigenvalues and eigenvectors. We generally indicate eigenvalues using the Greek letter lambda (&lambda;), and the formula that defines eigenvalues and eigenvectors with respect to a transformation is:\n",
+    "In cases like these, where a matrix transformation is the equivalent of a scalar-vector multiplication, the scalar-vector pairs that correspond to the matrix are known respectively as eigenvalues and eigenvectors. We generally indicate eigenvalues using the Greek letter lambda (&lambda;), and the formula that defines eigenvalues and eigenvectors with respect to a transformation is:\n",
     "\n",
     "$$ T(\\vec{v}) = \\lambda\\vec{v}$$\n",
     "\n",
@@ -2536,7 +2536,7 @@
     "\n",
     "$$A = Q \\Lambda Q^{-1}$$\n",
     "\n",
-    "Where ***A*** is a trasformation that can be applied to a vector in its current base, ***Q*** is a matrix of eigenvectors that defines a change of basis, and ***&Lambda;*** is a matrix with eigenvalues on the diagonal that defines the same linear transformation as ***A*** in the base defined by ***Q***.\n",
+    "Where ***A*** is a transformation that can be applied to a vector in its current base, ***Q*** is a matrix of eigenvectors that defines a change of basis, and ***&Lambda;*** is a matrix with eigenvalues on the diagonal that defines the same linear transformation as ***A*** in the base defined by ***Q***.\n",
     "\n",
     "Let's look at these in some more detail. Consider this matrix:\n",
     "\n",
@@ -2908,7 +2908,7 @@
    "source": [
     "So ***A*** and ***Q&Lambda;Q<sup>-1</sup>*** are equivalent.\n",
     "\n",
-    "If we view the intermediary stages of the decomposed transformation, you can see the transformation using ***A*** in the original base for ***v*** (orange to blue) and the transformation using ***&Lambda;*** in the change of basis decribed by ***Q*** (red to magenta):"
+    "If we view the intermediary stages of the decomposed transformation, you can see the transformation using ***A*** in the original base for ***v*** (orange to blue) and the transformation using ***&Lambda;*** in the change of basis described by ***Q*** (red to magenta):"
    ]
   },
   {
