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Math Help - Eigenvalues of a matrix involved in a linear matrix equality

  1. #1
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    Eigenvalues of a matrix involved in a linear matrix equality

    We know that:



    with , e : matrixes \in\Re^{nxn}; : generic eigenvalue of A;


    To be proved:



    with : positive scalar;


    Writing with ,

    we can prove , because .


    How to link eigenvalues of A to \overline{Q}?
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  2. #2
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    How about taking the "known" result (for matrices satisfying A^{\textsc t}P + PA = -Q ), and applying it with A+cI in place of A?
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  3. #3
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    You are right, good suggestion!
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