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Eigenvalues of hermitian matrix

  1. Dec 10, 2009 #1
    1. Let AH be the hermitian matrix of matrix A, and how the eigenvalues of AH be related to eigenvalues of A?



    3. what I have done is

    equation no.1: (AH-r1*I) * x1 = 0,
    And equation no.2: (A-r2*I) * x2 = 0

    time no.1 both sides by x2H
    ((A*x2)H-r1*x2H)* x1 = 0

    Then we have (conjugate (r2) -r1)*x2H*x1 = 0

    only if x1 and x2H are not orthogonal vectors,
    conjugate (r2) = r1

    so i just reach this conditional conclusion. but i am not sure what else can be know about the eigenvalues of hermitian matrix
     
  2. jcsd
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