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quiz7 - 4 Verify Cauchy-Schwarz on the vectors u = 1 1 1 1...

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MAS 3105 Quiz 7 November 9, 2010 1) Diagonalize the following matrix: A = 2 0 0 0 4 2 0 1 1 2) Prove that if A is diagonalizable, then A T is also diagonalizable. In particular, if A = PDP - 1 , then explicitly give the diagonalization of A T in terms of P and D . 3) Assume that A is a diagonalizable n × n matrix, and it has exactly one eigenvalue (let’s call it λ ). Show that A = λI n . 4) Verify Cauchy-Schwarz on the vectors
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Unformatted text preview: 4) Verify Cauchy-Schwarz on the vectors u = 1 1 1 1 and v = 1 1 − 1 . 5) If u = 1 1 1 1 , Fnd all the vectors v such that u · v = b u bb v b (in other words, Cauchy-Schwarz inequality is actually an equality)....
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