Is there a condition such that a symmetric matrix is "positive definite" for any component-wise positive vector?
There is a matrix $A$, and $A \in S^n$, $S$ denotes the real symmetric matrix set. What's the condition for $x^T A x > 0$, and $x \in R^n$, $|x| \neq 0$, and $x \succeq 0$ (component-wise positive).
Thank you.