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Unformatted text preview: A ) = ∑ n i =1 a ii . (a) Let C and D be any two n × n matrices. Prove that tr( CD ) =tr( DC ). (b) Prove that if A and B are similar n × n matrices, then tr( A ) =tr( B ). 3. Let M , N be n × n matrices and suppose that M is invertible. Denote A = MN and B = NM . Prove that A is similar to B . 4. From the Text § 5.1 # 2, 6, 16, 22, 25, 26, 27, 32 § 5.2 # 14, 16, 20, 24...
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This note was uploaded on 10/21/2010 for the course MATHEMATIC stats taught by Professor Various during the Spring '10 term at Waterloo.
 Spring '10
 various
 Linear Algebra, Algebra, Eigenvectors, Vectors

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