Timeline for why do we need to specify to symmetric matrix when defining real positive definite matrix? [closed]

6 events

when toggle format	what		by	license	comment
Dec 4, 2012 at 18:22	history	closed	Ryan Budney Pietro Majer Emil Jeřábek Chris Godsil Andreas Blass		not a real question
Dec 4, 2012 at 18:07	comment	added	Tobias Fritz		Can you provide the link to the Wikipedia page? If it really says that "This property implies that $M$ is an Hermitian matrix", then this is simply wrong and should be corrected. For example, if $M$ is anti-hermitian, then $z^T Mz=0$ for all $z$.
Dec 4, 2012 at 17:49	comment	added	Pietro Majer		The partial order for symmetric matrices is defined as $A\ge B$ iff $A-B$ is positive. If you try to define it for all matrices, most properties would be destroyed. Check the proofs.
Dec 4, 2012 at 17:47	answer	added	arbitUser1401		timeline score: 1
Dec 4, 2012 at 17:43	comment	added	kjetil b halvorsen		The point is that $z^T M z$ defines a quadratic form. If $M$ is not symmetric it can be replaced with $1/2(M+M^T)$ and with that matrix in place of $M$, exactly the same quadratic form results! check it.
Dec 4, 2012 at 17:08	history	asked	user29665	CC BY-SA 3.0