If C is an eigenvalue of a matrix A, with an associated eigenvector x, prove that Ck is an eigenvalue of the matrix Ak=AAA...(k products of A) with the associated eigenvector x, where k is any positive integer.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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If C is an eigenvalue of a matrix A, with an associated eigenvector x, prove that Ck is an eigenvalue of the matrix Ak=AAA...(k products of A) with the associated eigenvector x, where k is any positive integer.

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