An $n\times n$ Hermitian complex matrix $M$ is positive definite if $\langle x, Mx\rangle > 0$ for all $x\neq 0$ in $\mathbb C^n$ where $\langle\cdot,\cdot\rangle$ is the standard inner product on $\mathbb C^n$
If we allow the dot product to be zero, then $M$ is postive semidefinite.
Wikidata ID: Q1052034