Sign patterns allowing nilpotence of index 3 |
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Authors: | Yubin Gao Yanling Shao |
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Institution: | a Department of Mathematics, North University of China, Taiyuan, Shanxi 030051, PR China b Department of Mathematics and Statistics, Georgia State University, Atlanta, GA 30303-3083, USA |
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Abstract: | Suppose P is a property referring to a real matrix. We say that a sign pattern A allows P if there exists at least one matrix with the same sign pattern as A that has the property P. In this paper, we study sign patterns allowing nilpotence of index 3. Four methods for constructing sign patterns that allow nilpotence of index 3 are obtained. All tree sign patterns that allow nilpotence of index 3 are characterized. Sign patterns of order 3 that allow nilpotence are identified. |
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Keywords: | 15A18 05C15 |
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