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[appendix/math] Fix derivative of scalar with respect to matrix #13

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[appendix/math] Fix derivative of scalar with respect to matrix #13

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6 changes: 3 additions & 3 deletions content/appendix/math.md
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Expand Up @@ -136,7 +136,7 @@ and the derivative of $\bu$ with respect to $a$ is given by


$$
\dadb{\bu}{a} = \begin{pmatrix} \dadb{u_1}{a} \\ ... \\ \dadb{u_I}{a} \end{pmatrix} \R^I.
\dadb{\bu}{a} = \begin{pmatrix} \dadb{u_1}{a} \\ ... \\ \dadb{u_I}{a} \end{pmatrix} \in \R^I.
$$


Expand All @@ -160,7 +160,7 @@ and conversely the derivative of $a$ with respect to $\bX$ is given by


$$
\dadb{a}{\bX} = \begin{pmatrix} \dadb{a}{X_{11}} & ... & \dadb{a}{X_{1D}} \\ & ... & \\ \dadb{a}{X_{N1}} & ... & \dadb{a}{X_{ND}} \end{pmatrix} \in \R^{N \times D}.
\dadb{a}{\bX} = \begin{pmatrix} \dadb{a}{X_{11}} & ... & \dadb{a}{X_{N1}} \\ & ... & \\ \dadb{a}{X_{1D}} & ... & \dadb{a}{X_{ND}} \end{pmatrix} \in \R^{N \times D}.
$$


Expand Down Expand Up @@ -191,4 +191,4 @@ $$



Notice again that what we are taking the derivative *of* determines the first dimension(s) of the derivative and what we are taking the derivative with respect *to* determines the last.
Notice again that what we are taking the derivative *of* determines the first dimension(s) of the derivative and what we are taking the derivative with respect *to* determines the last.