4 13 4 13 0 3 0 2 1 1 at a 2 2 1 b is not normal 1 1

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Unformatted text preview: 3 −4 4 3 = 25 0 0 25 BB T = 1 2 −2 3 1 −2 2 3 = 5 −4 BT B = 1 −2 1 CC T = 0 0 2 3 1 1 0 1 −2 23 1 10 1 1 1 1 11 5 4 3 A is normal. −4 13 4 13 0 3 0 = 2 1 1 = = AT A ⇒ ⇒ 2 2 1 B is not normal. 1 1 1 1 CT C = 1 1 0 1 0 0 1 0 0 1 1 1 1 0 1 1 1 = 1 1 1 1 2 2 1 2 ⇒ 3 C is not normal. 2.79 √ √ 3/2 i −i/2 √ √/2 − 3/2 · = I ⇒A is unitary. A A= − 3/2 i/2 3/2 −i/2 1−i 1+i 1+i 1−i BH B = 1 · = I ⇒B is unitary. 4 1+i 1−i 1−i 1+i 1 −i 1−i 1 −i −1 − i 1 i 1 −1 − i · i 1 1 + i = I ⇒C CH C = 4 −1 − i 1 − i 0 1 + i −1 + i 0 H is unitary. 2.84 (a) 8 0 0 0 ,...
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This document was uploaded on 03/04/2014 for the course AMS 510 at SUNY Stony Brook.

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