# transpose of positive matrix is positive

how to prove it?

I am talking about matrixes which:

( Ax , x ) > 0 for any x not equals 0.

How to prove, that AT is also positive?

xT * A * x = ( xT * A * x )T

and what?

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Hint: Write the inner product as $x^T A x$ and use the fact that that expression is its own transpose (since it's a 1-by-1 matrix).