- #1
fanxiu
- 3
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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
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