Sign patterns that require ${\mathbb{H}}_n$ exist for each $n\ge 4$

Wei Gao, Zhongshan Li, Lihua Zhang

The refined inertia of a square real matrix $A$ is the ordered $4$-tuple $(n_{+},n_{-},n_z,2n_p)$, where $n_{+}$ (resp., $n_{-}$) is the number of eigenvalues of $A$ with positive (resp…