Unformatted text preview: T such that P T AP = T . 3. Let Q ( ~x ) = ~x T A~x with A = ± a b b c ² and det A 6 = 0. a) Prove that Q is positive deﬁnite if det A > 0 and a > 0. b) Prove that Q is negative deﬁnite if det A > 0 and a < 0. c) Prove that Q is indeﬁnite if det A < 0. 4. Let A and B be symmetric n × n matrices whose eigenvalues are all positive. Show that the eigenvalues of A + B are all positive....
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 Spring '10
 WILKIE
 Math, Matrices, Diagonal matrix, Orthogonal matrix, Normal matrix, Quadratic form, corresponding symmetric matrix

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