Unformatted text preview: 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 be an invertible symmetric matrix. Prove that if the quadratic form ~x T A~x is positive deﬁnite, then so it the quadratic form ~x T A1 ~x . 5. Let A be an n × n symmetric matrix and let ~x,~ y ∈ R n . Deﬁne < ~x,~ y > = ~x T A~ y . Prove that < ,> is an inner product on R n if and only if A is positive deﬁnite....
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 Spring '10
 WILKIE
 Math, Determinant, Diagonal matrix, Orthogonal matrix, Normal matrix, Quadratic form

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