Let A jk be an n n matrix with (not necessarily distinct) eigenvalues 1 , , n Show The polynomial matrix has the eigenvalues where j 1, ,n, and the same eigenvectors as A

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

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

The polynomial matrix

has the eigenvalues

where j = 1,· · ·,n, and the same eigenvectors as A.

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