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I have an array $V_{N*K}$ that I have a function defined over the elements of this matrix which is

$$ F=\sum_{j}^N\sum_{l}^N\sum_{k}^KV_{jk}\log\frac{V_{jk}}{V_{lk}}+V_{lk}\log\frac{V_{lk}}{V_{jk}} $$

The question is what is the derivative of this function, $F$ with respect to an element of array $V$, i.e., $V_{jk}$

Ali
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1 Answers1

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The rules of derivatives do not change.

$$ \frac{\partial F}{\partial V_{jk}}=\sum_j^N\sum_l^N\sum_k^K \log\frac{V_{jk}}{V_{lk}}+1-\frac{V_{lk}}{V_{jk}} $$

T.J. Gaffney
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  • Do you mean that for instance $$ \frac{\partial F}{\partial V_{1,1}}=\sum_{l}^N\log\frac{V_{1,1}}{V_{l,1}}+1-\frac{V_{l,1}}{V_{1,1}} $$ what happens if the sum of each row of $V$ is equal to 1. Then what would be your solution? Thanks –  Dec 31 '13 at 14:48