Let $A$ be an $n\times n$ symmetrix matrix, if $\forall i$,


$a\_{ii}\geq |a\_{ij}|,\forall j$


satisfies, can we say that $A$ is a positive semidefinite matrix? I tried to find a counter example, but failed.



Positive Semidefinite matrix
$$
A=\begin{bmatrix} 1 & 0 & 1 \\ 0 & 1 & 1 \\ 1 & 1 & 1 \end{bmatrix}
$$


