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?
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?
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).