Question: Let A = [ jk ] be an n n matrix with (not necessarily distinct) eigenvalues 1 , ,

Let A = [αjk] be an n × n matrix with (not necessarily distinct) eigenvalues λ1, · · · , λn. Show.

A - kI has the eigenvalues λ1 - k, · · ·, λn - k and the same eigenvectors as A.

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