Inertially arbitrary patterns
Yubin Gao, Yanling Shao · Linear and Multilinear Algebra · 2001
An n×n sign pattern matrix A is an inertially arbitrary pattern (IAP) if each non-negative triple (r s t) with r+s+t=n is the inertia of a matrix with sign pattern A. This paper considers the n×n(n2) skew-symmetric sign pattern Sn with each upper off-diagonal entry positive, the (1,1) entry negative, the (n n) entry positive, and every other diagonal entry zero. We prove that Sn is an IAP.