i) 1 Let A, B E Man (C) be two square matrices. 14 A~ B. Explain what it means that the matrices A and B are similar, i.e., Prove that if the matrices A and B are similar, then the the the set of of the matrix A is the same as the set of eigenvalues of the matrix B. Give an example of two matrices A, B € M2,2(C) such that eigenvalues A) A is not similar to B; and B) A and B have the same the same set of eigenvalues. Give a detailed justification to your answer.
i) 1 Let A, B E Man (C) be two square matrices. 14 A~ B. Explain what it means that the matrices A and B are similar, i.e., Prove that if the matrices A and B are similar, then the the the set of of the matrix A is the same as the set of eigenvalues of the matrix B. Give an example of two matrices A, B € M2,2(C) such that eigenvalues A) A is not similar to B; and B) A and B have the same the same set of eigenvalues. Give a detailed justification to your answer.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.6: The Matrix Of A Linear Transformation
Problem 7AEXP
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