1
$\begingroup$

Sylvester's criterion is stated and proved here. I was wondering: why is it stated only for Hermitian matrix? If $A$ is not hermitian, does it hold for A? If not, which implication(s) fail and can you provide a counterexample? And if not, is there any adjustment to be made to the proof to make it work?

$\endgroup$
1
$\begingroup$

Consider $$\begin{pmatrix} 1 & 1 \\ -100 & 1\end{pmatrix}$$

$\endgroup$
  • $\begingroup$ Indeed, for $(1,0)*A*(1,0)^T=1-100=-99$, yet the minors are positive. $\endgroup$ – MickG Jul 8 '15 at 18:40

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.