# A7 - C . 3. Prove that every n × n matrix A with real...

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Math 235 Assignment 7 Due: Wednesday, June 29th 1. For each of the following symmetric matrices, ﬁnd an orthogonal matrix P and diagonal matrix D such that P T AP = D . (a) A = ± 1 - 2 - 2 1 ² (b) A = 0 1 1 1 0 1 1 1 0 (c) A = 1 0 - 2 0 - 1 - 2 - 2 - 2 0 2. Prove that if A is orthogonal similar to B and B is orthogonally similar to C , then A is orthogonal similar to
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Unformatted text preview: C . 3. Prove that every n × n matrix A with real eigenvalues is orthogonally similar to a lower triangular matrix T . 4. Show that the following are equivalent for a symmetric matrix A : (1) A is orthogonal (2) A 2 = I (3) All the eigenvalues of A are ± 1...
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## This note was uploaded on 09/30/2011 for the course MATH 235 taught by Professor Celmin during the Spring '08 term at Waterloo.

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