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Matrix trace minimization and zeros

  1. Jan 23, 2013 #1
    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. jcsd
  3. Jan 24, 2013 #2
    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
     
  4. Jan 25, 2013 #3
    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
     
  5. Jan 25, 2013 #4
    LateX didn't work here

    How to present an equation here?

    Thank you

    Good Spirit
     
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