Two New Spectrally Arbitrary Pattern,

The sign pattern matrix is an important problem in the domain of the combinatorial mathematics. It involves the computer science, economics, sociology, biology, chemistry, and so on. And the research and future development of sign pattern matrix are widespread. In this paper, we give two different sign patten matrix which are spectrally arbitrary by using the Nilpotent-Jacobian screening method.In chapter 1, we introduce the history of development, the related knowledge, future development on the sign pattern matrices, our research problems and main results.In chapter 2, the author introduce one method that the method a sign pattern matrix is spectrally arbitrary, Nilpotent-Jacobian method.In chapter 3, we give two different sign patten matrix which are spectrally arbitrary by using the Nilpotent-Jacobian screening method, and we demonstrate that every super-pattern of them is a spectrally arbitrary sign pattern.