This commit is contained in:
Morten Hjorth-Jensen
2022-08-31 07:22:04 +02:00
parent ed7c56b77e
commit 4a6bce2d2e
9 changed files with 431 additions and 429 deletions
+1 -1
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@@ -404,7 +404,7 @@ MathJax.Hub.Config({
</center>
<br>
<center>
<h4>Aug 30, 2022</h4>
<h4>Aug 31, 2022</h4>
</center> <!-- date -->
<br>
+1 -1
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@@ -954,7 +954,7 @@ $$
<p>and</p>
$$
\frac{\partial (\boldsymbol{a}^T\boldsymbol{A}\boldsymbol{a})}{\partial \boldsymbol{a}} = (\boldsymbol{A}+\boldsymbol{A}^T)\boldsymbol{a},
\frac{\partial (\boldsymbol{a}^T\boldsymbol{A}\boldsymbol{a})}{\partial \boldsymbol{a}} = \boldsymbol{a}^T(\boldsymbol{A}+\boldsymbol{A}^T),
$$
<p>and</p>
+1 -1
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@@ -404,7 +404,7 @@ MathJax.Hub.Config({
</center>
<br>
<center>
<h4>Aug 30, 2022</h4>
<h4>Aug 31, 2022</h4>
</center> <!-- date -->
<br>
+2 -2
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@@ -184,7 +184,7 @@ MathJax.Hub.Config({
</center>
<br>
<center>
<h4>Aug 30, 2022</h4>
<h4>Aug 31, 2022</h4>
</center> <!-- date -->
<br>
@@ -4068,7 +4068,7 @@ $$
<p>and</p>
<p>&nbsp;<br>
$$
\frac{\partial (\boldsymbol{a}^T\boldsymbol{A}\boldsymbol{a})}{\partial \boldsymbol{a}} = (\boldsymbol{A}+\boldsymbol{A}^T)\boldsymbol{a},
\frac{\partial (\boldsymbol{a}^T\boldsymbol{A}\boldsymbol{a})}{\partial \boldsymbol{a}} = \boldsymbol{a}^T(\boldsymbol{A}+\boldsymbol{A}^T),
$$
<p>&nbsp;<br>
+2 -2
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@@ -330,7 +330,7 @@ MathJax.Hub.Config({
</center>
<br>
<center>
<h4>Aug 30, 2022</h4>
<h4>Aug 31, 2022</h4>
</center> <!-- date -->
<br>
@@ -3884,7 +3884,7 @@ $$
<p>and</p>
$$
\frac{\partial (\boldsymbol{a}^T\boldsymbol{A}\boldsymbol{a})}{\partial \boldsymbol{a}} = (\boldsymbol{A}+\boldsymbol{A}^T)\boldsymbol{a},
\frac{\partial (\boldsymbol{a}^T\boldsymbol{A}\boldsymbol{a})}{\partial \boldsymbol{a}} = \boldsymbol{a}^T(\boldsymbol{A}+\boldsymbol{A}^T),
$$
<p>and</p>
+2 -2
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@@ -407,7 +407,7 @@ MathJax.Hub.Config({
</center>
<br>
<center>
<h4>Aug 30, 2022</h4>
<h4>Aug 31, 2022</h4>
</center> <!-- date -->
<br>
@@ -3961,7 +3961,7 @@ $$
<p>and</p>
$$
\frac{\partial (\boldsymbol{a}^T\boldsymbol{A}\boldsymbol{a})}{\partial \boldsymbol{a}} = (\boldsymbol{A}+\boldsymbol{A}^T)\boldsymbol{a},
\frac{\partial (\boldsymbol{a}^T\boldsymbol{A}\boldsymbol{a})}{\partial \boldsymbol{a}} = \boldsymbol{a}^T(\boldsymbol{A}+\boldsymbol{A}^T),
$$
<p>and</p>
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@@ -2915,7 +2915,7 @@ Show that
and
!bt
\[
\frac{\partial (\bm{a}^T\bm{A}\bm{a})}{\partial \bm{a}} = (\bm{A}+\bm{A}^T)\bm{a},
\frac{\partial (\bm{a}^T\bm{A}\bm{a})}{\partial \bm{a}} = \bm{a}^T(\bm{A}+\bm{A}^T),
\]
!et
and
@@ -2953,3 +2953,5 @@ and written out in terms of the vector $\bm{x}$ we have
\frac{\partial f(\bm{x})}{\partial \bm{x}}= \bm{A}.
\]
!et