Can someone help with this exercise? Given a symmetric n x n positive definite matrix A, and an arbitrary non- singular n x n matrix P, show that P'AP is positive definite.
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We know that , , and . So we want to show P'AP>0. Let , since Similarly, and since P is invertible this implies . Now self-adjoint should be given probably from a theorem, but here's a proof. If A=A', then (P'AP)'=P'A'P''=P'AP.
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