TY - JFULL
AU - Ling Zhang and Feng Liu
PY - 2019/1/
TI - Several Spectrally Non-Arbitrary Ray Patterns of Order 4
T2 - International Journal of Mathematical and Computational Sciences
SP - 222
EP - 226
VL - 13
SN - 1307-6892
UR - https://publications.waset.org/pdf/10010962
PU - World Academy of Science, Engineering and Technology
NX - Open Science Index 156, 2019
N2 - 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.
ER -