From c7837c4b87eba04d5dd06229d50cc9a8858d899f Mon Sep 17 00:00:00 2001 From: curioushruti Date: Mon, 19 Oct 2020 21:47:22 -0700 Subject: [PATCH] Fix derivative of scalar with respect to matrix + add missing `belongs to` symbol for derivative of vector with respect to scalar --- content/appendix/math.md | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/content/appendix/math.md b/content/appendix/math.md index 2825ca1..d249a94 100644 --- a/content/appendix/math.md +++ b/content/appendix/math.md @@ -136,7 +136,7 @@ and the derivative of $\bu$ with respect to $a$ is given by $$ -\dadb{\bu}{a} = \begin{pmatrix} \dadb{u_1}{a} \\ ... \\ \dadb{u_I}{a} \end{pmatrix} \R^I. +\dadb{\bu}{a} = \begin{pmatrix} \dadb{u_1}{a} \\ ... \\ \dadb{u_I}{a} \end{pmatrix} \in \R^I. $$ @@ -160,7 +160,7 @@ and conversely the derivative of $a$ with respect to $\bX$ is given by $$ -\dadb{a}{\bX} = \begin{pmatrix} \dadb{a}{X_{11}} & ... & \dadb{a}{X_{1D}} \\ & ... & \\ \dadb{a}{X_{N1}} & ... & \dadb{a}{X_{ND}} \end{pmatrix} \in \R^{N \times D}. +\dadb{a}{\bX} = \begin{pmatrix} \dadb{a}{X_{11}} & ... & \dadb{a}{X_{N1}} \\ & ... & \\ \dadb{a}{X_{1D}} & ... & \dadb{a}{X_{ND}} \end{pmatrix} \in \R^{N \times D}. $$ @@ -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. \ No newline at end of file +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.