Relating to a symmetric $n\times n $ real matrix $(M)$ such that the scalar $x^TMx\ge 0\ \forall x\in \Bbb{R}^n\backslash \{0\}$

If $M$ is a positive semidefinite matrix then it has some additional properties which can be found in this Wikipedia article. You can also use this tag if one or more of these properties leads back to $M$ being positive-semidefinite.