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Unformatted text preview: det A = 1. Let A be a 3 × 3 real rotation matrix. Show that 1 is an eigen value. (10 points) (8) Find the invariant factors of the following matrix; 1 0 0 0 0 2 0 2 0 4 (10 points) (9) Show that an n × n matrix A is c for some constant c iﬀ it commutes with every n × n matrix B (10 points) (10) Let A be an n × n complex matrix. Suppose that A 2 = A . Show that A is selfadjoint iﬀ A * A = AA * 5 (10 points) (11) Find the Jordan canonical form of the following matrix over the complex numbers C ; 2 0 0 1 2 0 1 1 1 (10 points) (12) Describe all bilinear forms f on R 3 which satisfy f ( α,β ) =f ( β,α ) for all α,β . 6...
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 Spring '09
 Linear Algebra, Matrices, FP

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