Primitive non-powerful sign pattern matrices with base 2 |
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| Authors: | Longqin Wang Hongping Ma |
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| Affiliation: | 1. Department of Mathematics , Chuzhou University , Chuzhou, 239012, P.R. China;2. School of Mathematical Sciences , Xuzhou Normal University , Xuzhou, 221116, P.R. China |
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| Abstract: | A sign pattern matrix M with zero trace is primitive non-powerful if for some positive integer k, M k ?=?J #. The base l(M) of the primitive non-powerful matrix M is the smallest integer k. By considering the signed digraph S whose adjacent matrix is the primitive non-powerful matrix M, we will show that if l(M)?=?2, the minimum number of non-zero entries of M is 5n???8 or 5n???7 depending on whether n is even or odd. |
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| Keywords: | base matrix sign pattern primitive non-powerful signed digraph |
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