- #1
randommacuser
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Homework Statement
Let E be the exchange matrix (ones on the anti-diagonal, zeroes elsewhere). Suppose A is symmetric and positive definite. Show that B = EAE is positive definite.
Homework Equations
The Attempt at a Solution
I've tried showing directly that for any conformable vector h, h'Bh > 0 whenever h'Ah > 0. This looks like a dead end. I suspect the easiest way to get the result is to show all the eigenvalues of B are positive, using the fact that all the eigenvalues of A are positive. However, I don't know how to show this.