Question
Given a matrix
where α and β are non-zero complex numbers, find its eigenvalues and eigenvec-
tors. Find the respective conditions for (a) the eigenvalues to be real and (b) the
eigenvectors to be orthogonal. Show that the conditions are jointly satisfied if
and only if A is Hermitian.
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Transcribed Image Text

Given a matrix where α and β are non-zero complex numbers, find its eigenvalues and eigenvec- tors. Find the respective conditions for (a) the eigenvalues to be real and (b) the eigenvectors to be orthogonal. Show that the conditions are jointly satisfied if and only if A is Hermitian.