Question: If B = M-1AM, prove that the square matrices A and B have the same eigenvalues. Also, express the eigenvectors of B in terms of

If B = M-1AM, prove that the square matrices A and B have the same eigenvalues. Also, express the eigenvectors of B in terms of the eigenvectors of A. Start with the eigenvalue equation for A, replace A by its expression in terms of B, and multiply the resulting equation by M-1 on the left to obtain the eigenvalue equation for B.

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Multiplication of B M 1 AM by M on the left gives MB MM 1 AM IAM AM Multiplication of MB ... View full answer

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