From 6f858c92c140675bcae6802b29b3d4a48c7c85f1 Mon Sep 17 00:00:00 2001
From: Morten Hjorth-Jensen <morten.hjorth-jensen@fys.uio.no>
Date: Mon, 6 Sep 2021 16:58:52 +0200
Subject: [PATCH] updating

---
 doc/pub/week35/html/week35-reveal.html       |   6 +++---
 doc/pub/week35/html/week35-solarized.html    |   6 +++---
 doc/pub/week35/html/week35.html              |   6 +++---
 doc/pub/week35/ipynb/ipynb-week35-src.tar.gz | Bin 191 -> 192 bytes
 doc/pub/week35/ipynb/week35.ipynb            |   6 +++---
 doc/src/week35/week35.do.txt                 |   6 +++---
 6 files changed, 15 insertions(+), 15 deletions(-)

diff --git a/doc/pub/week35/html/week35-reveal.html b/doc/pub/week35/html/week35-reveal.html
index d42a73f55..f14fc4647 100644
--- a/doc/pub/week35/html/week35-reveal.html
+++ b/doc/pub/week35/html/week35-reveal.html
@@ -2654,10 +2654,10 @@ $$
 <p>&nbsp;<br>
 
 <p>
-If we then compute the expectation value
+If we then compute the expectation value (note the \( 1/n \) factor instead of \( 1/(n-1) \))
 <p>&nbsp;<br>
 $$
-\mathbb{E}[\boldsymbol{X}^T\boldsymbol{X}] = \frac{1}{n}\boldsymbol{X}^T\boldsymbol{X}=\begin{bmatrix}
+\mathbb{E}[\boldsymbol{X}^T\boldsymbol{X}] = \frac{1}{n}\boldsymbol{X}^T\boldsymbol{X}=\frac{1}{n}\begin{bmatrix}
 x_{00}^2+x_{01}^2 & x_{00}x_{10}+x_{01}x_{11}\\
 x_{10}x_{00}+x_{11}x_{01} & x_{10}^2+x_{11}^2\\
 \end{bmatrix},
@@ -2675,7 +2675,7 @@ $$
 
 where we wrote <p>&nbsp;<br>
 $$\boldsymbol{C}[\boldsymbol{x}_0,\boldsymbol{x}_1] = \boldsymbol{C}[\boldsymbol{x}]$$
-<p>&nbsp;<br> to indicate that this the covariance of the vectors \( \boldsymbol{x} \) of the design/feature matrix \( \boldsymbol{X} \).
+<p>&nbsp;<br> to indicate that this is the covariance of the vectors \( \boldsymbol{x} \) of the design/feature matrix \( \boldsymbol{X} \).
 
 <p>
 It is easy to generalize this to a matrix \( \boldsymbol{X}\in {\mathbb{R}}^{n\times p} \).
diff --git a/doc/pub/week35/html/week35-solarized.html b/doc/pub/week35/html/week35-solarized.html
index bbcada960..02bae429b 100644
--- a/doc/pub/week35/html/week35-solarized.html
+++ b/doc/pub/week35/html/week35-solarized.html
@@ -2666,9 +2666,9 @@ x_{10} & x_{11}\\
 $$
 
 <p>
-If we then compute the expectation value
+If we then compute the expectation value (note the \( 1/n \) factor instead of \( 1/(n-1) \))
 $$
-\mathbb{E}[\boldsymbol{X}^T\boldsymbol{X}] = \frac{1}{n}\boldsymbol{X}^T\boldsymbol{X}=\begin{bmatrix}
+\mathbb{E}[\boldsymbol{X}^T\boldsymbol{X}] = \frac{1}{n}\boldsymbol{X}^T\boldsymbol{X}=\frac{1}{n}\begin{bmatrix}
 x_{00}^2+x_{01}^2 & x_{00}x_{10}+x_{01}x_{11}\\
 x_{10}x_{00}+x_{11}x_{01} & x_{10}^2+x_{11}^2\\
 \end{bmatrix},
@@ -2681,7 +2681,7 @@ $$
              \end{bmatrix},
 $$
 
-where we wrote $$\boldsymbol{C}[\boldsymbol{x}_0,\boldsymbol{x}_1] = \boldsymbol{C}[\boldsymbol{x}]$$ to indicate that this the covariance of the vectors \( \boldsymbol{x} \) of the design/feature matrix \( \boldsymbol{X} \).
+where we wrote $$\boldsymbol{C}[\boldsymbol{x}_0,\boldsymbol{x}_1] = \boldsymbol{C}[\boldsymbol{x}]$$ to indicate that this is the covariance of the vectors \( \boldsymbol{x} \) of the design/feature matrix \( \boldsymbol{X} \).
 
 <p>
 It is easy to generalize this to a matrix \( \boldsymbol{X}\in {\mathbb{R}}^{n\times p} \).
diff --git a/doc/pub/week35/html/week35.html b/doc/pub/week35/html/week35.html
index 3efd21e35..2fbf430b4 100644
--- a/doc/pub/week35/html/week35.html
+++ b/doc/pub/week35/html/week35.html
@@ -2671,9 +2671,9 @@ x_{10} & x_{11}\\
 $$
 
 <p>
-If we then compute the expectation value
+If we then compute the expectation value (note the \( 1/n \) factor instead of \( 1/(n-1) \))
 $$
-\mathbb{E}[\boldsymbol{X}^T\boldsymbol{X}] = \frac{1}{n}\boldsymbol{X}^T\boldsymbol{X}=\begin{bmatrix}
+\mathbb{E}[\boldsymbol{X}^T\boldsymbol{X}] = \frac{1}{n}\boldsymbol{X}^T\boldsymbol{X}=\frac{1}{n}\begin{bmatrix}
 x_{00}^2+x_{01}^2 & x_{00}x_{10}+x_{01}x_{11}\\
 x_{10}x_{00}+x_{11}x_{01} & x_{10}^2+x_{11}^2\\
 \end{bmatrix},
@@ -2686,7 +2686,7 @@ $$
              \end{bmatrix},
 $$
 
-where we wrote $$\boldsymbol{C}[\boldsymbol{x}_0,\boldsymbol{x}_1] = \boldsymbol{C}[\boldsymbol{x}]$$ to indicate that this the covariance of the vectors \( \boldsymbol{x} \) of the design/feature matrix \( \boldsymbol{X} \).
+where we wrote $$\boldsymbol{C}[\boldsymbol{x}_0,\boldsymbol{x}_1] = \boldsymbol{C}[\boldsymbol{x}]$$ to indicate that this is the covariance of the vectors \( \boldsymbol{x} \) of the design/feature matrix \( \boldsymbol{X} \).
 
 <p>
 It is easy to generalize this to a matrix \( \boldsymbol{X}\in {\mathbb{R}}^{n\times p} \).
diff --git a/doc/pub/week35/ipynb/ipynb-week35-src.tar.gz b/doc/pub/week35/ipynb/ipynb-week35-src.tar.gz
index 76b4c6ce14003561849fc4ea3794f866bf04d0e1..f1916750fc61205132376517d589bc66e79fb0c0 100644
GIT binary patch
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zh;_mv+4d@jLZcnOz~Hr$20^GEL{Ug5wGx-GHTq;kW25lb$9SISd0%?~Hiykw00;m8
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delta 148
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C`#^*M

diff --git a/doc/pub/week35/ipynb/week35.ipynb b/doc/pub/week35/ipynb/week35.ipynb
index 86a83a788..55177c1d4 100644
--- a/doc/pub/week35/ipynb/week35.ipynb
+++ b/doc/pub/week35/ipynb/week35.ipynb
@@ -3402,7 +3402,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "If we then compute the expectation value"
+    "If we then compute the expectation value (note the $1/n$ factor instead of $1/(n-1)$)"
    ]
   },
   {
@@ -3410,7 +3410,7 @@
    "metadata": {},
    "source": [
     "$$\n",
-    "\\mathbb{E}[\\boldsymbol{X}^T\\boldsymbol{X}] = \\frac{1}{n}\\boldsymbol{X}^T\\boldsymbol{X}=\\begin{bmatrix}\n",
+    "\\mathbb{E}[\\boldsymbol{X}^T\\boldsymbol{X}] = \\frac{1}{n}\\boldsymbol{X}^T\\boldsymbol{X}=\\frac{1}{n}\\begin{bmatrix}\n",
     "x_{00}^2+x_{01}^2 & x_{00}x_{10}+x_{01}x_{11}\\\\\n",
     "x_{10}x_{00}+x_{11}x_{01} & x_{10}^2+x_{11}^2\\\\\n",
     "\\end{bmatrix},\n",
@@ -3439,7 +3439,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "where we wrote $$\\boldsymbol{C}[\\boldsymbol{x}_0,\\boldsymbol{x}_1] = \\boldsymbol{C}[\\boldsymbol{x}]$$ to indicate that this the covariance of the vectors $\\boldsymbol{x}$ of the design/feature matrix $\\boldsymbol{X}$.\n",
+    "where we wrote $$\\boldsymbol{C}[\\boldsymbol{x}_0,\\boldsymbol{x}_1] = \\boldsymbol{C}[\\boldsymbol{x}]$$ to indicate that this is the covariance of the vectors $\\boldsymbol{x}$ of the design/feature matrix $\\boldsymbol{X}$.\n",
     "\n",
     "It is easy to generalize this to a matrix $\\boldsymbol{X}\\in {\\mathbb{R}}^{n\\times p}$.\n",
     "\n",
diff --git a/doc/src/week35/week35.do.txt b/doc/src/week35/week35.do.txt
index 0038d9465..5d31e1f9a 100644
--- a/doc/src/week35/week35.do.txt
+++ b/doc/src/week35/week35.do.txt
@@ -2147,10 +2147,10 @@ x_{10} & x_{11}\\
 \]
 !et
 
-If we then compute the expectation value
+If we then compute the expectation value (note the $1/n$ factor instead of $1/(n-1)$)
 !bt
 \[
-\mathbb{E}[\bm{X}^T\bm{X}] = \frac{1}{n}\bm{X}^T\bm{X}=\begin{bmatrix}
+\mathbb{E}[\bm{X}^T\bm{X}] = \frac{1}{n}\bm{X}^T\bm{X}=\frac{1}{n}\begin{bmatrix}
 x_{00}^2+x_{01}^2 & x_{00}x_{10}+x_{01}x_{11}\\
 x_{10}x_{00}+x_{11}x_{01} & x_{10}^2+x_{11}^2\\
 \end{bmatrix},
@@ -2164,7 +2164,7 @@ which is just
              \end{bmatrix},
 \]
 !et
-where we wrote $$\bm{C}[\bm{x}_0,\bm{x}_1] = \bm{C}[\bm{x}]$$ to indicate that this the covariance of the vectors $\bm{x}$ of the design/feature matrix $\bm{X}$.
+where we wrote $$\bm{C}[\bm{x}_0,\bm{x}_1] = \bm{C}[\bm{x}]$$ to indicate that this is the covariance of the vectors $\bm{x}$ of the design/feature matrix $\bm{X}$.
 
 It is easy to generalize this to a matrix $\bm{X}\in {\mathbb{R}}^{n\times p}$.