Negative-Definite Matrix

Definition

$M\prec 0\iff \forall \mathbf{z}\ne 0,{\mathbf{z}}^{⊺}M\mathbf{z}<0$

Matrix $M$, in which ${\mathbf{z}}^{⊺}M\mathbf{z}$ is negative for every non-zero column vector $\mathbf{z}$ is a negative-definite matrix