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Unformatted text preview: ± ≤ j − 1, since all we have done to q k +1 is to add a multiple of q j to it, and q j is orthogonal to q ± . Thus, after iteration j , q ∗ ± q new k +1 = 0 for ± ≤ j , and the induction is complete when j = k and k = n − 1. CHALLENGE 5.10. (a) We verify that Q is unitary by showing that its conjugate transpose is its inverse: Q ∗ Q = ( I − 2 uu ∗ )( I − 2 uu ∗ ) = I − 4 uu ∗ + 4 uu ∗ uu ∗ = I , since u ∗ u = 1. ±or the second part, we compute v ∗ z = ( z ∗ − α ∗ e T 1 ) z = z ∗ z − α ∗ z 1 = z ∗ z − e − iθ ± z ± e iθ ζ = z ∗ z − ± z ± ζ,...
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This note was uploaded on 01/21/2012 for the course MAP 3302 taught by Professor Dr.robin during the Fall '11 term at University of Florida.
 Fall '11
 Dr.Robin

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