1bSet8 - (2) For some a C , a is an eigenvalue of A of...

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CALIFORNIA INSTITUTE OF TECHNOLOGY Department of Mathematics Math 1b, Analytical; Homework Set 8 Due: 10am, Monday, March 8, 2010 1. Problem 14 on page 126 of the text. 2. Prove that for each 2 by 2 matrix A over C , exactly one of the following holds: (1) For some a C , A = aI is a scalar matrix with eigenvalue a of multiplicity 2.
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Unformatted text preview: (2) For some a C , a is an eigenvalue of A of multiplicity 2 and A is similar to a 1 a . (3) There are distinct a,b C such that A has eigenvalues a,b and A is similar to the diagonal matrix a b . 3. Problem 1 on page 141 of the text. 1...
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This note was uploaded on 03/03/2011 for the course MATH 1B taught by Professor Aschbacher during the Winter '07 term at Caltech.

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