Consider a square matrix $A$ with each element $a_{ij}<0$ $\forall i, \forall j$.
Is it true that $A$ is negative definite? Do we need $A$ symmetric to establish that?
2026-03-25 09:33:46.1774431226
Square matrix with all negative elements is negative definite?
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Consider the following $2\times 2$ matrix:
$$\begin{bmatrix} -3 & -4 \\ -4 & -2 \\ \end{bmatrix}$$
This matrix is indefinite, but with all elements negative. By definition, in order to define definiteness of a matrix, that matrix has to be symmetric.