AME525_HW_02_Solutions_020906

AME525_HW_02_Solutions_020906 - AME525 HW#2 Section 8.1...

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Unformatted text preview: AME525 HW#2 Section 8.1 Section 8.2 Section 8.3 16. T A A A = ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡ − − − = => ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡ − − − = − 9 / 8 9 / 4 9 / 1 9 / 1 9 / 4 9 / 8 9 / 4 9 / 7 9 / 4 9 / 8 9 / 1 9 / 4 9 / 4 9 / 4 9 / 7 9 / 1 9 / 8 9 / 4 1 Section 8.4 Section 8.5 8) 1 ) det( 2 + = ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ − − = − => ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ = λ λ λ λ i i I A i i A 1 2 = + λ => i ± = 2 , 1 λ . All eigenvalues are imaginary and have absolute value 1, then A is a skew-Hermitian and unitary matrix. For i = λ , = ⎭ ⎬ ⎫ ⎩ ⎨ ⎧ ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ − − y x i i i i => , ⎭ ⎬ ⎫ ⎩ ⎨ ⎧ = 1 1 } { 1 X For i − = λ = ⎭ ⎬ ⎫ ⎩ ⎨ ⎧ ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ y x i i i i => . ⎭ ⎬ ⎫ ⎩ ⎨ ⎧ − = 1 1 } { 2 X 10) λ λ λ λ λ λ 4 1 1 1 1 ) det( 1 1 1 1 3 + − = ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡ − − + − − + − = − => ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡ − + − + = i i i i I...
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This note was uploaded on 04/27/2010 for the course -1 -1 taught by Professor -1 during the Spring '07 term at USC.

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AME525_HW_02_Solutions_020906 - AME525 HW#2 Section 8.1...

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