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I have a matrix kernel function which I am trying to find the derivative to. Function is K = c * exp[-1/2 * (P(X1 - X2))' * P(X1 -X2)] where uppercase are matrices and lower case are scalars (and ' denotes transpose). I'm trying to find dK/dP. I'm pretty rusty on matrix calculus, can anyone give me a hand here?

Thanks

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    Your notation is not very clear. Is $P$ a matrix? then did you mean something like $K(P) = c \exp[-\frac12 \| P(X_1 - X_2) \|^2]$? In that case you should probably write (P(X1-X2))', the transpose should be around everything and maybe a trace before it? Is P symmetric or not?2012-06-13
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    I was assuming this is a matrix valued function. If that's true I'd undelete my (by now corrected) answer. If @passerby51 assumption is correct, the derivative is just $$ D_V K = -1/2K \langle V(X_1-X_2), P(X_1-X_2)\rangle$$ with $\langle.,.\rangle$ the scalar product on the vector space of matrices.2012-06-13
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    Sorry yeah the transpose is around the whole thing. P is not symmetric.2012-06-13
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    Yeah it is a matrix valued function. I didn't quite get a chance to see your deleted answer Thomas. What was it? Thanks for the response guys.2012-06-13
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    undeleted my reply.2012-06-13
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    Sorry this is going to be kind of dumb, but Thomas, what is V?2012-06-13
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    if this is a matrix valued function, you have to take the derivative in direction of a matrix $V$. $D_V K(X) = \frac{d}{d t}K(X+tV)|_{t=0}$2012-06-13
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    (And the factor $1/2$ in my previous comment is not correct)2012-06-13

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