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.
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$\begingroup$ A standard result guarantees the positivity is diagonal dominance. $\endgroup$– M. LinJul 1, 2014 at 19:51
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$$ A=\begin{bmatrix} 1 & 0 & 1 \\ 0 & 1 & 1 \\ 1 & 1 & 1 \end{bmatrix} $$
answered Jul 1, 2014 at 9:54