Several spectrally arbitrary ray patterns |
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| Authors: | Ling Zhang Ting-Zhu Huang Zhongshan Li Jing-Yue Zhang |
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| Institution: | 1. School of Mathematical Sciences , University of Electronic Science and Technology of China , Chengdu , Sichuan 611731 , P.R. China lvjinliang415@163.com;3. School of Mathematical Sciences , University of Electronic Science and Technology of China , Chengdu , Sichuan 611731 , P.R. China;4. Department of Mathematics and Statistics , Georgia State University , Atlanta , GA 30303-3083 , USA |
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| Abstract: | A ray pattern A of order n is said to be spectrally arbitrary if given any monic nth degree polynomial f(x) with coefficients from ?, there exists a matrix realization of A such that its characteristic polynomial is f(x). An n?×?n ray pattern A is said to be minimally spectrally arbitrary if replacing any nonzero entry of A by zero destroys this property. In this article, several families of ray patterns are presented and proved to be minimally spectrally arbitrary. We also show that for n?≥?5, when A n is spectrally arbitrary, then it is minimally spectrally arbitrary. |
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| Keywords: | spectrally arbitrary nilpotent matrix ray pattern |
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