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.
Follow Math Help Forum on Facebook and Google+
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.
View Tag Cloud