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Math Help - Regarding spectral radius of products of matrices subject to some restrictions

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    Regarding spectral radius of products of matrices subject to some restrictions

    Simulations confirm my claim, but I can't prove it. Please help me out!
    The problem in multivariate case is a half page long pdf file. The univariate case is as follows.
    For given (real valued) scalars, (a11,..a22), (real-valued) x11,..,x22 must satisfy the following restrictions.

    a11*x11+a12*x12=1,
    a12*x12+a22*x22=1,

    Let S_A=[a11^2 a12^2;a21^2 a22^2] and
    S_X=[x11^2 x21^2;x12^2 x22^2]

    Let rho(B)=maximum eigenvalue of B in absolute value.

    My claim is that
    the maximum eigenvalue of rho(S_A)<1 if and only if rho(S_X)>1 for S_X with x11,..x22 are subject to the constraints above.
    Attached Files Attached Files
    Last edited by sc719; July 13th 2011 at 02:31 AM.
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