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Whats a quick way to work the below (and problems similar) out?

For me to take this derivative it involves a lot of time and boring calculation, there has to be a better way.

This is taken from the solutions to Chris Bishop's Pattern Recognition and Machine learning:

from Pattern Recogition and Machine Learning

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up vote 13 down vote accepted

There is something called the Matrix Cookbook, which includes a lot of identities and matrix derivatives. So if we look at eq. (88) of the Matrix Cookbook,

$$\frac{\partial}{\partial A} (\mathbf{x} -\mathbf{A}\mathbf{s})^T\mathbf{W}(\mathbf{x} -\mathbf{A}\mathbf{s}) = -2\mathbf{W}(\mathbf{x}-\mathbf{A}\mathbf{s})\mathbf{s}^T$$

we see that this directly refers to your problem, if we assume $\Sigma^{-1}$ is a covariance matrix and therefore symmetric.

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Thank you! That is very helpful :) – user3490171 Feb 25 at 10:02
    
I made a couple of formatting changes - you might like to know that you can start and terminate a piece of Latex with $$ ... $$ if you want an equation to be centre-aligned. – Silverfish Feb 25 at 11:25

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