Fixed typos

StephenElston · StephenElston · commit f4e4a038d700 · 2018-07-07T14:17:59.000-07:00
diff --git a/Module03/03-05-Transformations Eigenvectors and Eigenvalues.ipynb b/Module03/03-05-Transformations Eigenvectors and Eigenvalues.ipynb
@@ -1224,7 +1224,7 @@
     "\n",
     "So our eigenvalue-eigenvector scalar multiplications do indeed correspond to our matrix-eigenvector dot-product transformations.\n",
     "\n",
-    "Here's the equivalent code in Python, using the ***eVals*** and ***eVecs*** variables you generated in the previous code cell:"
+    "Here's the equivalent code in R using the previous results:"
    ]
   },
   {
@@ -1716,7 +1716,7 @@
     "$$ 2 \\times \\begin{bmatrix}-1 \\\\ 0\\end{bmatrix} = \\begin{bmatrix}-2 \\\\ 0\\end{bmatrix}  \\;\\;\\;and\\;\\;\\; \\begin{bmatrix}2 & 0\\\\0 & 2\\end{bmatrix} \\cdot \\begin{bmatrix}-1 \\\\ 0\\end{bmatrix} = \\begin{bmatrix}-2 \\\\ 0\\end{bmatrix} $$\n",
     "\n",
     "\n",
-    "Now let's use Pythonto verify and plot these transformations:"
+    "Now let's use R to verify and plot these transformations:"
    ]
   },
   {
@@ -2186,7 +2186,7 @@
     "\n",
     "$$ 1 \\times \\begin{bmatrix}-0.70710678 \\\\ 0.70710678\\end{bmatrix} = \\begin{bmatrix}-0.70710678\\\\0.70710678\\end{bmatrix}  \\;\\;\\;and\\;\\;\\; \\begin{bmatrix}2 & 1\\\\1 & 2\\end{bmatrix} \\cdot \\begin{bmatrix}-0.70710678 \\\\ 0.70710678\\end{bmatrix} = \\begin{bmatrix}-0.70710678\\\\0.70710678\\end{bmatrix} $$\n",
     "\n",
-    "With more complex examples like this, it's generally easier to do it with Python:"
+    "With more complex examples like this, it's generally easier to use a tool like R:"
    ]
   },
   {
@@ -2542,7 +2542,7 @@
     "\n",
     "$$A=\\begin{bmatrix}3 & 2\\\\1 & 0\\end{bmatrix}$$\n",
     "\n",
-    "***Q*** is a matrix in which each column is an eigenvector of ***A***; which as we've seen previously, we can calculate using Python:"
+    "***Q*** is a matrix in which each column is an eigenvector of ***A***; which as we've seen previously, we can calculate using R:"
    ]
   },
   {
@@ -3352,7 +3352,7 @@
     "\n",
     "$$A^{-1}=\\begin{bmatrix}-0.4472136 & -0.70710678 \\\\-0.89442719 & 0.70710678 \\end{bmatrix}\\cdot\\begin{bmatrix}0.2 & 0\\\\0 & -1\\end{bmatrix}\\cdot\\begin{bmatrix}-0.74535599 & 0.47140452\\\\-0.94280904 & -0.74535599\\end{bmatrix}$$\n",
     "\n",
-    "Let's calculate that in Python:"
+    "Let's calculate that with R:"
    ]
   },
   {
@@ -3455,7 +3455,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "Which is the orriginal matrix A. \n",
+    "Which is the original matrix A. \n",
     "\n",
     "You can also use R verify that:\n",
     "\n",

Original file line number	Diff line number	Diff line change
`@@ -1224,7 +1224,7 @@`
`1224`	`1224`	`"\n",`
`1225`	`1225`	`"So our eigenvalue-eigenvector scalar multiplications do indeed correspond to our matrix-eigenvector dot-product transformations.\n",`
`1226`	`1226`	`"\n",`
`1227`		`- "Here's the equivalent code in Python, using the *eVals* and *eVecs* variables you generated in the previous code cell:"`
	`1227`	`+ "Here's the equivalent code in R using the previous results:"`
`1228`	`1228`	`]`
`1229`	`1229`	`},`
`1230`	`1230`	`{`
`@@ -1716,7 +1716,7 @@`
`1716`	`1716`	`"$$ 2 \\times \\begin{bmatrix}-1 \\\\ 0\\end{bmatrix} = \\begin{bmatrix}-2 \\\\ 0\\end{bmatrix} \\;\\;\\;and\\;\\;\\; \\begin{bmatrix}2 & 0\\\\0 & 2\\end{bmatrix} \\cdot \\begin{bmatrix}-1 \\\\ 0\\end{bmatrix} = \\begin{bmatrix}-2 \\\\ 0\\end{bmatrix} $$\n",`
`1717`	`1717`	`"\n",`
`1718`	`1718`	`"\n",`
`1719`		`- "Now let's use Pythonto verify and plot these transformations:"`
	`1719`	`+ "Now let's use R to verify and plot these transformations:"`
`1720`	`1720`	`]`
`1721`	`1721`	`},`
`1722`	`1722`	`{`
`@@ -2186,7 +2186,7 @@`
`2186`	`2186`	`"\n",`
`2187`	`2187`	`"$$ 1 \\times \\begin{bmatrix}-0.70710678 \\\\ 0.70710678\\end{bmatrix} = \\begin{bmatrix}-0.70710678\\\\0.70710678\\end{bmatrix} \\;\\;\\;and\\;\\;\\; \\begin{bmatrix}2 & 1\\\\1 & 2\\end{bmatrix} \\cdot \\begin{bmatrix}-0.70710678 \\\\ 0.70710678\\end{bmatrix} = \\begin{bmatrix}-0.70710678\\\\0.70710678\\end{bmatrix} $$\n",`
`2188`	`2188`	`"\n",`
`2189`		`- "With more complex examples like this, it's generally easier to do it with Python:"`
	`2189`	`+ "With more complex examples like this, it's generally easier to use a tool like R:"`
`2190`	`2190`	`]`
`2191`	`2191`	`},`
`2192`	`2192`	`{`
`@@ -2542,7 +2542,7 @@`
`2542`	`2542`	`"\n",`
`2543`	`2543`	`"$$A=\\begin{bmatrix}3 & 2\\\\1 & 0\\end{bmatrix}$$\n",`
`2544`	`2544`	`"\n",`
`2545`		`- "*Q* is a matrix in which each column is an eigenvector of *A*; which as we've seen previously, we can calculate using Python:"`
	`2545`	`+ "*Q* is a matrix in which each column is an eigenvector of *A*; which as we've seen previously, we can calculate using R:"`
`2546`	`2546`	`]`
`2547`	`2547`	`},`
`2548`	`2548`	`{`
`@@ -3352,7 +3352,7 @@`
`3352`	`3352`	`"\n",`
`3353`	`3353`	`"$$A^{-1}=\\begin{bmatrix}-0.4472136 & -0.70710678 \\\\-0.89442719 & 0.70710678 \\end{bmatrix}\\cdot\\begin{bmatrix}0.2 & 0\\\\0 & -1\\end{bmatrix}\\cdot\\begin{bmatrix}-0.74535599 & 0.47140452\\\\-0.94280904 & -0.74535599\\end{bmatrix}$$\n",`
`3354`	`3354`	`"\n",`
`3355`		`- "Let's calculate that in Python:"`
	`3355`	`+ "Let's calculate that with R:"`
`3356`	`3356`	`]`
`3357`	`3357`	`},`
`3358`	`3358`	`{`
`@@ -3455,7 +3455,7 @@`
`3455`	`3455`	`"cell_type": "markdown",`
`3456`	`3456`	`"metadata": {},`
`3457`	`3457`	`"source": [`
`3458`		`- "Which is the orriginal matrix A. \n",`
	`3458`	`+ "Which is the original matrix A. \n",`
`3459`	`3459`	`"\n",`
`3460`	`3460`	`"You can also use R verify that:\n",`
`3461`	`3461`	`"\n",`