# Thread: matrix trace minimizations and zeros

1. ## 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

2. ## 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

Best regards

GoodSpirit

3. ## Re: matrix trace minimization and zeros

Hello again,

I forgot to say that P' and S' are the transpose of P and S respectively.
and ^-1 is the inverse operation.

I've been using matrix derivatives...

What do you think about that?

best regards

GoodSpirit