Inertially arbitrary patterns |
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Authors: | Yubin Gao Yanling Shao |
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Institution: |
a Department of Mathematics, North China Institute of Technology, Taiyuan, Shanxi, 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 (rst) with r+s+t=n is the inertia of a matrix with sign pattern A. This paper considers the n×n(n≥2) skew-symmetric sign pattern Sn with each upper off-diagonal entry positive, the (1,1) entry negative, the (nn) 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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