Suppose two n × n matrices A and B are similar.(a) (8 pts) Show that A and B have the same eigenvalues
Question
Solution 1
Two matrices A and B are said to be similar if there exists an invertible matrix P such that B = P^-1 * A * P.
Let's assume λ is an eigenvalue of A, with corresponding eigenvector x. Then we have:
A * x = λ * x
We can multiply both sides of this equation by P^-1 and P (on the left and right resp Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study prob
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