# Matrix trace minimization and zeros

1. Jan 23, 2013

### GoodSpirit

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

2. Jan 24, 2013

### GoodSpirit

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 in particular.
By the way, the matrix A is symmetric too.

Many thanks

3. Jan 25, 2013

### GoodSpirit

Hello,

Trying to update the equation presentation.

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

A is positive definite

I've using matrix derivatives

What do you think?

All the best

GoodSpirit

4. Jan 25, 2013

### GoodSpirit

LateX didn't work here

How to present an equation here?

Thank you

Good Spirit