hw8 - u Verify that this defines an inner product on C 3...

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Winter 2011 Math 67 Linear Algebra Homework 8 Axler Problems 1.3, 1.9. (Hint for 1.3 a j b j = ja j b j / j .) Problem. Write [1 , 2 , 3 , 4 i ] as av + w where v = [1 , 0 , - 1 , - 2 i ] and h v,w i = 0. Problem. Consider the matrix Q = 1 2 i 2 8 i - i - i 2 For u,v C 3 , define h u,v i by the formula u t Q ¯ v . That is, take the conjugate of v , right mulitply by Q and then take the dot product with
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Unformatted text preview: u . Verify that this defines an inner product on C 3 . Problem. Let h , i be the inner product of the previous problem. Apply Gram-Schmitt orthogonalization to the standard basis e 1 ,e 2 ,e 3 of C 3 . 1...
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