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$\begingroup$

how to prove it?

I am talking about matrixes which satisfy:

$( Ax , x ) > 0\quad \text{ for any}\quad \;x \neq 0.$

How to prove that $A^T\;$ is also positive?

$x^T A x = ( x^T A x )^T$

and what?

1 Answers 1

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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).

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    Thx, I understood!2011-01-17