Hi,

For any Hermitian matrixT,

z*T zis real and is >= 0. The * denotes conjugate transpose.

I understand that if any of the eigenvalues ofTare equal to zero, thenTis positive semi-definite (z*T z>= 0).

What I don't get is whyTis positive definite (z*T z> 0) iff all of it's eigen values are > 0; even if all eigenvalues are > 0, couldn't there still be azwhich leads to semi-definiteness?

Thanks.