@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 = {233 - 236}, 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}, }