Ling Zhang and Feng Liu
Several Spectrally NonArbitrary Ray Patterns of Order 4
223 - 226
2019
13
12
International Journal of Mathematical and Computational Sciences
https://publications.waset.org/pdf/10010962
https://publications.waset.org/vol/156
World Academy of Science, Engineering and Technology
A matrix is called a ray pattern matrix if its entries are either 0 or a ray in complex plane which originates from 0. A ray pattern A of order n is called spectrally arbitrary if the complex matrices in the ray pattern class of A give rise to all possible nth degree complex polynomial. Otherwise, it is said to be spectrally nonarbitrary ray pattern. We call that a spectrally arbitrary ray pattern A of order n is minimally spectrally arbitrary if any nonzero entry of A is replaced, then A is not spectrally arbitrary. In this paper, we find that is not spectrally arbitrary when n equals to 4 for any &theta; which is greater than or equal to 0 and less than or equal to n. In this article, we give several ray patterns A(&theta;) of order n that are not spectrally arbitrary for some &theta; which is greater than or equal to 0 and less than or equal to n. by using the nilpotentJacobi method. One example is given in our paper.
Open Science Index 156, 2019