Inertially arbitrary patterns |
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Authors: | Yubin Gao Yanling Shao |
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Affiliation: | 1. Department of Mathematics , North China Institute of Technology , Taiyuan, Shanxi, 030051, People's Republic of China ybgao@public.ty.sx.cn;3. Department of Mathematics , North China Institute of Technology , Taiyuan, Shanxi, 030051, People's Republic of China |
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Abstract: | 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. |
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Keywords: | Sign pattern Inertia Skew-symmetric sign pattern AMS Classification: 15A18 |
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