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 May 11th, 2013, 08:33 AM #1 Newbie   Joined: Dec 2012 Posts: 3 Thanks: 0 Gram matrix Hi everbody, i have to proof, that for a comlex matrix A is invertible if $B:=A\overline{A}^T$ is positive definite. That means for every $x \in \mathbb{C}^n$ and $x \not= 0$ we know that $x^T B \overline{x} >0.$ Do you have any ideas how to proof this? I'm not allowed to use any criterion based on eigenvalues. Thank you very much

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