Re: Matrix derivative

In article <1166789958.652578.169980@xxxxxxxxxxxxxxxxxxxxxxxxxxx>,
seppl <basti2@xxxxxxxxxxxxxx> wrote:
Hi all,

I'd like to know the derivative of

log A w.r.t A ,where log is the matrix logarithm and how to compute it.

Generally, one uses differentials. But log(A+dA) is not
an easy expression otherwise.

To see this, consider log (I - X - dX), where X is small
(all characteristic roots less than 1 in absolute value.
This is -\sum (X+dX)^n/n. Now if we expand this, and
just keep the first order terms in dX, we find the
negative of the differential of the logarithm is

dX + (X*dX + dX*X)/2 + (X^2*dX + X*dX*X + dX*X^2)/3 + ...

This does not simplify unless X and dX commute.

Furthermore I would like to know if there is a good online-available
reference for matrix derivatives.

Thanks in advance.
Seppl



--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
hrubin@xxxxxxxxxxxxxxx Phone: (765)494-6054 FAX: (765)494-0558
.

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