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Matrix trace minimization and zeros

by GoodSpirit
Tags: matrix, minimization, trace, zeros
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GoodSpirit
#1
Jan23-13, 08:21 AM
P: 19
Hello, :)

I would like to minimize and find the zeros of the function F(S,P)=trace(S-SPí(A+ PSPí)^-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
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GoodSpirit
#2
Jan24-13, 06:03 AM
P: 19
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
GoodSpirit
#3
Jan25-13, 06:03 AM
P: 19
Hello,

Trying to update the equation presentation.

[tex] F(S,P)=tr(S-S P^T(A+PSP^T)^-1 PS) [/tex]

A is positive definite

I've using matrix derivatives

What do you think?

All the best

GoodSpirit

GoodSpirit
#4
Jan25-13, 06:04 AM
P: 19
Matrix trace minimization and zeros

LateX didn't work here

How to present an equation here?

Thank you

Good Spirit


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