Let $A \in \mathbb{R}^{n \times n}$ be a symmetric indefinite matrix. Furthermore, we let $e_i$ be the $i^{th}$ vector for standard basis. Is it possible to have $(e_i-e_j)^{T}A(e_i-e_j)>0$ for all $1\le i,j\le n$?
2026-03-30 23:30:19.1774913419
Quadratic form of a symmetric indefinite matrix
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$$ \left( \begin{array}{rrr} 3 & -2 & -2 \\ -2 & 3 & -2 \\ -2 & -2 & 3 \end{array} \right) $$