@article{(Open Science Index):https://publications.waset.org/pdf/10010962,
	  title     = {Several Spectrally Non-Arbitrary Ray Patterns of Order 4},
	  author    = {Ling Zhang and  Feng Liu},
	  country	= {},
	  institution	= {},
	  abstract     = {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 non-arbitrary 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 θ which is greater than or equal to 0 and less than or equal to n. In this article, we give several ray patterns A(θ) of order n that are not spectrally arbitrary for some θ which is greater than or equal to 0 and less than or equal to n. by using the nilpotent-Jacobi method. One example is given in our paper.
},
	    journal   = {International Journal of Mathematical and Computational Sciences},
	  volume    = {13},
	  number    = {12},
	  year      = {2019},
	  pages     = {223 - 226},
	  ee        = {https://publications.waset.org/pdf/10010962},
	  url   	= {https://publications.waset.org/vol/156},
	  bibsource = {https://publications.waset.org/},
	  issn  	= {eISSN: 1307-6892},
	  publisher = {World Academy of Science, Engineering and Technology},
	  index 	= {Open Science Index 156, 2019},
	}