Let A = [ jk ] be an n n matrix with (not necessarily distinct) eigenvalues
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Let A = [αjk] be an n × n matrix with (not necessarily distinct) eigenvalues λ1, · · · , λn. Show.
The polynomial matrix
has the eigenvalues
where j = 1,· · ·,n, and the same eigenvectors as A.
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To show that the polynomial matrix PA has the same eigenvectors as A and that its eigenvalues are given by Pj where j is an eigenvalue of A we need to ...View the full answer
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