HW2_602_2011

HW2_602_2011 - Math 602 (2011) Homework 2 1. a) Find a...

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Math 602 (2011) Homework 2 1. a) Find a unitary similarity transformation which brings the lower triangular matrix ± a 0 b c ² to upper triangular form. b) Find a unitary similarity transformation which brings B = 1 0 1 1 0 1 1 2 0 0 0 0 0 0 2 0 1 1 0 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0 1 1 into upper triangular form. c) What are the eigenvalues of B ? 2. Suppose that T is an 3 × 3 upper triangular matrix. Show that if TT * = T * T , then T must be diagonal. Note: the same result holds for a general n × n upper triangular matrix. 3. Let T be a linear operator on V , and let h , i be an inner product on
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