By definition, a symmetric matrix $\mathrm{A} \in \mathbb{R}^{n \times n}$ is positive definite if for all $\mathrm{x} \in \mathbb{R}^n \setminus \{\mathrm{0}\}$, $\mathrm{x}^{\mathrm{T}} \mathrm{A} \mathrm{x}>\mathrm{0}$. I also understand that a positive definite matrix is nonsingular.
Can we draw the conclusion that if a general square matrix is singular, then it is not positive definite?
EDIT
I think that my question is conversely different from the one posted here, in the sense that I need to know if we can say the opposite; i.e., if $\mathrm{A}$ is singular, then $(\Rightarrow)$, is $\mathrm{A}$ not positive definite?
Thanks.