**Unformatted text preview: **characteristic polynomials of similar matrices are the same). (ii) Conclude that the traces of similar matrices are the same. 6. Do one of the following problems. I: Let A be a real symmetric matrix and let v and w be eigenvectors for diﬀerent eigenvalues λ and μ , λ 6 = μ . Show that v and w are orthogonal. II. Suppose that there are n linearly independent vectors in R n which are eigen-vectors for the n × n matrix A . Prove that there is an invertible n × n matrix P so that P-1 AP is a diagonal matrix....

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