Research On The Arbitrariness Of Matrix Patterns Of Several Symbolic Patterns

Sign pattern matrix is a more active research topic in combinatorial mathematics, it is very important. It has wide application in many subjects,such as economics,chemistry,biology,computer science,and sociology. In this paper, we study a new class of sign pattern and three classes of complex sign patterns,then prove that they are minimally spectrally arbitrary sign patterns.At the beginning of this article we introduce the origin and the development of sign pattern matrix, some relevant conceptions and conclusions.The main results of this paper are also introduced.The main research work is reflected in the other parts of this paper includes that:In the second part we ues N-J and N-C methods contrastively to prove a sign pattern matix is minimally spectrally arbitrary in detail.We present a complex sign pattern matrix and prove that it is minimally spectrally arbitrary in the third part.We prove another two complex sign patterns are minimally spectrally arbitrary in the fourth part.