#### Vol. 12, No. 7, 2019

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Sign pattern matrices that allow inertia $\mathbb{S}_{n}$

### Adam H. Berliner, Derek DeBlieck and Deepak Shah

Vol. 12 (2019), No. 7, 1229–1240
##### Abstract

Sign pattern matrices of order $n$ that allow inertias in the set ${\mathbb{S}}_{n}$ are considered. All sign patterns of order 3 (up to equivalence) that allow ${\mathbb{S}}_{3}$ are classified and organized according to their associated directed graphs. Furthermore, a minimal set of such matrices is found. Then, given a pattern of order $n$ that allows ${\mathbb{S}}_{n}$, a construction is given that generates families of irreducible sign patterns of order $n+1$ that allow ${\mathbb{S}}_{n+1}$.

##### Keywords
sign pattern, zero-nonzero pattern, inertia, digraph, Jacobian
##### Mathematical Subject Classification 2010
Primary: 15B35, 15A18, 05C50
Secondary: 05C20