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4. Let A, B be two square matrices of the same size over a field F such that AB = BA. If v is an eigenvector of A, show that the product (B v) is also an eigenvector of A with the same eigenvalue as v.

4. Let A, B be two square matrices of the same size over a field F such that AB = BA. If v is an eigenvector of A, show that the product (B v) is also an eigenvector of A with the same eigenvalue as v.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.3: Eigenvalues And Eigenvectors Of N X N Matrices
Problem 24EQ
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4. Let A, B be two square matrices of the same size over a field F such that AB = BA. If v is an eigenvector of A, show that the product (B v) is also an eigenvector of A with the same eigenvalue as v.
Transcribed Image Text:4. Let A, B be two square matrices of the same size over a field F such that AB = BA. If v is an eigenvector of A, show that the product (B v) is also an eigenvector of A with the same eigenvalue as v.
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