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Sign patterns that allow diagonalizability revisited |
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| Authors: | Xin-Lei Feng Zhongshan Li Jun Luo Yubin Gao |
| Institution: | 1. College of Mathematics and information Science , Leshan Normal University , Leshan , Sichuan 614000 , P.R. China;2. School of Mathematical Sciences , University of Electronic Science and Technology of China , Chengdu , Sichuan 611731 , P.R. China;3. Department of Mathematics , North University of China , Taiyuan , Shanxi 030051 , P.R. China;4. Department of Mathematics and Statistics , Georgia State University , Atlanta , GA 30302 , USA;5. School of Mathematical Sciences , University of Electronic Science and Technology of China , Chengdu , Sichuan 611731 , P.R. China;6. Department of Mathematics , North University of China , Taiyuan , Shanxi 030051 , P.R. China |
| Abstract: | Characterization of sign patterns that allow diagonalizability has been a long-standing open problem. In this article, necessary and sufficient conditions for a sign pattern to allow diagonalizability are obtained, in terms of allowing related properties. Some properties of normal sign patterns are considered. In particular, it is shown that normal sign patterns of order up to 3 allow diagonalizability. Two combinatorial necessary conditions for a sign pattern to allow diagonalizability are also presented. |
| Keywords: | sign pattern allow diagonalizability allow normality distinct eigenvalues minimum rank maximum rank generalized permutation maximum cycle length |