# Is this matrix positive semidefinite (Symmetric matrix, with particular pattern)

Let's consider a symmetric matrix A.

If for each row, the diagonal entry is equal or larger than the magnitude of any other element, that is

$$a_{ii} \geq |a_{ij}| \quad\text{for all rows } i \text{ and entries } j , \,$$

then the matrix is positive semi-definite

$$\begin{pmatrix} 1 & 0.9 & 0.9 \\ 0.9 & 1 & 0.1 \\ 0.9 & 0.1 & 1 \end{pmatrix}$$ is indefinite, since the eigenvalues are $$0.9$$ and $$(21 \pm \sqrt{649})/20$$.