Proof of matrix trace inequality

From: Jay Jeon (jeon30c_at_gmail.com)
Date: 03/13/05

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    Date: 13 Mar 2005 04:28:06 -0800

    A, B : hermitian positive definite n by n matrix
    U : n by m matrix ( m<=n)
    U^H U=I

    trace{(U^H A U)^(-1) U^H B U} <= trace{A^(-1) B}

    equality when m=n

    is it possible to prove this?

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