Derivative with respect to matrix

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# Derivative with respect to matrix

Submitted by neilamezghni on Tue, 04/27/2010 - 14:54

Forums:

Hello,

1- How to determine a derivative of a function with respect to matrix?

2- For example let a function f such that

f(C)= x'Cy + x'C'y + x'C'ACy

where x and y are vectors and C and A are matrix and (') is the opertor transpose.

what is the derivative of f with respect to C?

Thank you.

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## Versions

(v1) by neilamezghni 2010-04-27

## Re: Derivative with respect to matrix

Hello,

If I understand there isn't a derivative with respect to matrix like my example.

## Re: Derivative with respect to matrix

There is.

http://en.wikipedia.org/wiki/FrÃ©chet_derivative

## Re: Derivative with respect to matrix

At point C in direction B the derivative is

Df(C)(B)=x'By+x'B'y+x'B'ACy+x'C'ABy