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Given the weight graph $G(V,E,w)$, we define the adjacency matrix $A$ by $$A_{ij}=\begin{cases} w_{ij},&\text{if }(i,j) \in E, \\ 0 & \text{otherwise}.\end{cases}$$ The degree matrix of a weighted graph is a diagonal matrix $D$ such that $$D_{ii}=\sum_j A_{ij}.$$ Which is the derivative of $P=D^{-1/2}AD^{-1/2}$ with respect to $A$? $$\frac{\partial P}{{\partial\ A}}=\frac{\partial\big(D^{-1/2}AD^{-1/2}\big)}{\partial\ A}$$

I was wondering if any one could help me to find out the answer.

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    You can add equations using [LaTeX](https://en.wikibooks.org/wiki/LaTeX). – 2017-01-10
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    Go to Google and type in "Matrix Cookbook." – 2017-01-10
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    I typed it according to "Matrix Cookbook". – 2017-01-10

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