Derivatives of a the Matrix diagonal function

Question

If A is a not diagonal but symetric matrix and diag() is a function such that returns the diagonal, i.e. diag(A) is a matrix of zeros except on the diagonal. Im interested in the derivative of vec(diag(A)) with respect to x where A is a function of the vector x. So, how do I do This in the best way?

Thanks in advance!

You should clarify what "A is a function of the vector x" means. Some funcion in particular? Each component of the matrix is an indepent function of x? — leonbloy, Dec 13 '12 at 19:40

score 6 · Answer 1 · answered Dec 13 '12 at 19:44

6

The derivative of the $(i,i)$ entry of $\text{diag}(A)$ is the same as the derivative of the $(i,i)$ entry of $A$. The derivative of the $(i,j)$ entry of $\text{diag}(A)$ for $i \ne j$ is $0$.

answered Dec 13 '12 at 19:44

Robert Israel

448,999

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@ Robert. Interesting. So you are saying $\nabla diag(A)= diag(\nabla(A))$? – user25004 Jan 08 '13 at 02:58
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Of course. The derivatives are element-wise operations. – Robert Israel Jan 09 '13 at 05:26

Derivatives of a the Matrix diagonal function

1 Answers1