# Questions tagged [matrix-calculus]

Matrix calculus deals with the problems of differentiating (possibly matrix-valued) functions of matrices

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### Taking derivative for RNN back propogation

I am trying to understand the derivation of backpropagation for recurrent neural networks (RNNs) from this source: https://github.com/go2carter/nn-learn/blob/master/grad-deriv-tex/rnn-grad-deriv.pdf ...
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### Vectorized gradients for neural networks: matrix multiplication

In Stanford's 231N course, they discuss computing a vectorized form of the gradient of the loss function w.r.t. the matrix $W$ as the derivative of the matrix multiplication $WX$ w.r.t. $W$ multiplied ...
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### Derivative of $x^T A^Ty$ with respect to $\Sigma$ where $A$ is (an upper triangle matrix and ) Cholesky decomposition of $\Sigma$

I would like to evaluate: $$\frac{ \partial x^T A^Ty}{\partial \Sigma}$$ where $A$ is a Cholesky decomposition of $\Sigma$ and an upper triangle matrix such that $\Sigma = A^T A$, $x$ and $y$ are a ...
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### What are the 2nd derivatives of the log multivariate normal density?

I develop open-source statistical software (http://openmx.psyc.virginia.edu/), but matrix calculus is not my strong point. I need the 1st and 2nd derivatives of the log multivariate normal density. I ...