update week 35

This commit is contained in:
Morten Hjorth-Jensen
2021-09-06 22:26:00 +02:00
parent da58b1525f
commit ed47ea2760
6 changed files with 10 additions and 10 deletions
+2 -2
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@@ -2658,8 +2658,8 @@ If we then compute the expectation value (note the \( 1/n \) factor instead of \
<p>&nbsp;<br>
$$
\mathbb{E}[\boldsymbol{X}^T\boldsymbol{X}] = \frac{1}{n}\boldsymbol{X}^T\boldsymbol{X}=\frac{1}{n}\begin{bmatrix}
x_{00}^2+x_{01}^2 & x_{00}x_{10}+x_{01}x_{11}\\
x_{10}x_{00}+x_{11}x_{01} & x_{10}^2+x_{11}^2\\
x_{00}^2+x_{10}^2 & x_{00}x_{01}+x_{10}x_{11}\\
x_{01}x_{00}+x_{11}x_{10} & x_{01}^2+x_{11}^2\\
\end{bmatrix},
$$
<p>&nbsp;<br>
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@@ -2667,8 +2667,8 @@ $$
If we then compute the expectation value (note the \( 1/n \) factor instead of \( 1/(n-1) \))
$$
\mathbb{E}[\boldsymbol{X}^T\boldsymbol{X}] = \frac{1}{n}\boldsymbol{X}^T\boldsymbol{X}=\frac{1}{n}\begin{bmatrix}
x_{00}^2+x_{01}^2 & x_{00}x_{10}+x_{01}x_{11}\\
x_{10}x_{00}+x_{11}x_{01} & x_{10}^2+x_{11}^2\\
x_{00}^2+x_{10}^2 & x_{00}x_{01}+x_{10}x_{11}\\
x_{01}x_{00}+x_{11}x_{10} & x_{01}^2+x_{11}^2\\
\end{bmatrix},
$$
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@@ -2672,8 +2672,8 @@ $$
If we then compute the expectation value (note the \( 1/n \) factor instead of \( 1/(n-1) \))
$$
\mathbb{E}[\boldsymbol{X}^T\boldsymbol{X}] = \frac{1}{n}\boldsymbol{X}^T\boldsymbol{X}=\frac{1}{n}\begin{bmatrix}
x_{00}^2+x_{01}^2 & x_{00}x_{10}+x_{01}x_{11}\\
x_{10}x_{00}+x_{11}x_{01} & x_{10}^2+x_{11}^2\\
x_{00}^2+x_{10}^2 & x_{00}x_{01}+x_{10}x_{11}\\
x_{01}x_{00}+x_{11}x_{10} & x_{01}^2+x_{11}^2\\
\end{bmatrix},
$$
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@@ -3411,8 +3411,8 @@
"source": [
"$$\n",
"\\mathbb{E}[\\boldsymbol{X}^T\\boldsymbol{X}] = \\frac{1}{n}\\boldsymbol{X}^T\\boldsymbol{X}=\\frac{1}{n}\\begin{bmatrix}\n",
"x_{00}^2+x_{01}^2 & x_{00}x_{10}+x_{01}x_{11}\\\\\n",
"x_{10}x_{00}+x_{11}x_{01} & x_{10}^2+x_{11}^2\\\\\n",
"x_{00}^2+x_{10}^2 & x_{00}x_{01}+x_{10}x_{11}\\\\\n",
"x_{01}x_{00}+x_{11}x_{10} & x_{01}^2+x_{11}^2\\\\\n",
"\\end{bmatrix},\n",
"$$"
]
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@@ -2151,8 +2151,8 @@ If we then compute the expectation value (note the $1/n$ factor instead of $1/(n
!bt
\[
\mathbb{E}[\bm{X}^T\bm{X}] = \frac{1}{n}\bm{X}^T\bm{X}=\frac{1}{n}\begin{bmatrix}
x_{00}^2+x_{01}^2 & x_{00}x_{10}+x_{01}x_{11}\\
x_{10}x_{00}+x_{11}x_{01} & x_{10}^2+x_{11}^2\\
x_{00}^2+x_{10}^2 & x_{00}x_{01}+x_{10}x_{11}\\
x_{01}x_{00}+x_{11}x_{10} & x_{01}^2+x_{11}^2\\
\end{bmatrix},
\]
!et