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Unformatted text preview: AME525 HW#2 Section 8.1 Section 8.2 Section 8.3 16. T A A A = âŽ¥ âŽ¥ âŽ¥ âŽ¦ âŽ¤ âŽ¢ âŽ¢ âŽ¢ âŽ£ âŽ¡ âˆ’ âˆ’ âˆ’ = => âŽ¥ âŽ¥ âŽ¥ âŽ¦ âŽ¤ âŽ¢ âŽ¢ âŽ¢ âŽ£ âŽ¡ âˆ’ âˆ’ âˆ’ = âˆ’ 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 + = âŽ¥ âŽ¦ âŽ¤ âŽ¢ âŽ£ âŽ¡ âˆ’ âˆ’ = âˆ’ => âŽ¥ âŽ¦ âŽ¤ âŽ¢ âŽ£ âŽ¡ = Î» Î» Î» Î» i i I A i i A 1 2 = + Î» => i Â± = 2 , 1 Î» . All eigenvalues are imaginary and have absolute value 1, then A is a skewHermitian and unitary matrix. For i = Î» , = âŽ âŽ¬ âŽ« âŽ© âŽ¨ âŽ§ âŽ¥ âŽ¦ âŽ¤ âŽ¢ âŽ£ âŽ¡ âˆ’ âˆ’ y x i i i i => , âŽ âŽ¬ âŽ« âŽ© âŽ¨ âŽ§ = 1 1 } { 1 X For i âˆ’ = Î» = âŽ âŽ¬ âŽ« âŽ© âŽ¨ âŽ§ âŽ¥ âŽ¦ âŽ¤ âŽ¢ âŽ£ âŽ¡ y x i i i i => . âŽ âŽ¬ âŽ« âŽ© âŽ¨ âŽ§ âˆ’ = 1 1 } { 2 X 10) Î» Î» Î» Î» Î» Î» 4 1 1 1 1 ) det( 1 1 1 1 3 + âˆ’ = âŽ¥ âŽ¥ âŽ¥ âŽ¦ âŽ¤ âŽ¢ âŽ¢ âŽ¢ âŽ£ âŽ¡ âˆ’ âˆ’ + âˆ’ âˆ’ + âˆ’ = âˆ’ => âŽ¥ âŽ¥ âŽ¥ âŽ¦ âŽ¤ âŽ¢ âŽ¢ âŽ¢ âŽ£ âŽ¡ âˆ’ + âˆ’ + = 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.
 Spring '07
 1

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