Eigenvalues of hermitian matrix

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
 

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