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Eigenvalues of hermitian matrix
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[QUOTE="fanxiu, post: 2484751, member: 218670"] [b]1. Let A[SUP]H[/SUP] be the hermitian matrix of matrix A, and how the eigenvalues of A[SUP]H[/SUP] be related to eigenvalues of A? [/b] [b]3. what I have done is equation no.1: (A[SUP]H[/SUP]-r[SUB]1[/SUB]*I) * x[SUB]1[/SUB] = 0, And equation no.2: (A-r[SUB]2[/SUB]*I) * x[SUB]2[/SUB] = 0 time no.1 both sides by x[SUB]2[/SUB][SUP]H[/SUP] ((A*x[SUB]2[/SUB])[SUP]H[/SUP]-r[SUB]1[/SUB]*x[SUB]2[/SUB][SUP]H[/SUP])* x[SUB]1[/SUB] = 0 Then we have (conjugate (r[SUB]2[/SUB]) -r[SUB]1[/SUB])*x[SUB]2[/SUB][SUP]H[/SUP]*x[SUB]1[/SUB] = 0 only if x[SUB]1[/SUB] and x[SUB]2[/SUB][SUP]H[/SUP] are not orthogonal vectors, conjugate (r[SUB]2[/SUB]) = r[SUB]1[/SUB] so i just reach this conditional conclusion. but i am not sure what else can be know about the eigenvalues of hermitian matrix[/b] [/QUOTE]
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Eigenvalues of hermitian matrix
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