# Matrix trace minimizations and zeros

### Matrix trace minimizations and zeros

Hello,

I would like to minimize and find the zeros of the function F(S,P)=trace(S-SP’(A+ PSP’)^-1PS) in respect to S and P.
S is symmetric square matrix.
P is a rectangular matrix
Could you help me?
Thank you very much

All the best

GoodSpirit

Guest

### Re: Matrix trace minimizations and zeros

Hello everybody,

Perhaps I should explain a little bit.

The aim is to minimize an error metric and preferentially drive it to zero.
This should be done as function of S and P, as function of their rank and dimensions.
By the way, the matrix A is symmetric too.

Many thanks
GoodSpirit

Posts: 2
Joined: Wed Jan 23, 2013 9:52 am

### Re: Matrix trace minimization and zeros

Hello just updating the equation presentation in Latex

$F(S,P)=tr(S-SP^T(A+PSP^T)^{-1}PS)$

A is also positive definite

I've using matrix derivatives ...

What do you think?

All the best

GoodSpirit
GoodSpirit

Posts: 2
Joined: Wed Jan 23, 2013 9:52 am