Matrix non-singular -symmetric (A) has eigenvalues E(n) .Then A^{-1} has eigenvalues 1/E(n) . Give the proof if anyone knows.
Prof B.Rath
Prof .Damion
Your answer sounds correct .If you have time ,pl, take any (3×3) matrix and calculate
S . Many thanks for your valuable idea.
Prof B.Rath
For complex matrix if ( aij = -aij )it gives real eigenvalue.Here I consiser all non-diagonal elements complex. .Is it a general case ?If so give a proof.However , I notice
it is not the general case.
For complex( aij= aji ) eigenvalues may be real or complex .H=p^2 + ix , is symmetric but not the enery spectrum.
Please give your views on my understanding. The spectra of H=p^2 + ix is complex
The matrix is symmetric .So how do we say that symmetric matrix gives real eigenvalues ?
Many thanks for reply.
H=p^2 +ix on diagonalisation has complex eigenvalues.This means diagonal elements complex .So Tagaki's theorem is no longer valid. Hemce how to address complex
eigenvalues of symmetric matrix. Secondly give one or two page xerox by mail or
RG. I have not seen that theorem .Any way your help in this regard is highly appreciated. Incase I write a paper ,I would like to give an ACK.So give your Academic address.
Thanks.
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