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.

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

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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