Lecture38 - BA(b trace αA B = α trace A trace B 4 Suppose that S ∈ C n × n is an invertible matrix Show that SAS-1 and A have the same

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Exercises December 8, 2010 1. If the characteristic polynomial of a matrix A is ( t 2 - 4) 2 ( t + 1) 5 , then compute the size of the matrix, its eigenvalues, trace and determinant. 2. Show that ( ST ) * = T * S * and that ( αT ) * = αT * . 3. If A,B C n , then prove that (a) trace( AB ) = trace(
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Unformatted text preview: BA ). (b) trace( αA + B ) = α trace( A ) + trace( B ) 4. Suppose that S ∈ C n × n is an invertible matrix. Show that SAS-1 and A have the same characteristic polynomial, eigenvalues, trace, and determinant. 1...
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This document was uploaded on 10/29/2011 for the course MATH 204 at Vanderbilt.

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