About Two Special Symbols Arbitrary Pattern Matrix Spectral Studies

Sign pattern matrix is a very active research topic in combinatorial mathematics.Thisthesis mainly use Nilpotent-Jacobi method to study two classes of special spectrally arbitrarysign pattern matrices. This thesis is organized as follows.Chapter1briefly describes the origin and research significance of sign pattern matrix.Then some basic conceptions, relevant conclusions and main results in this thesis areintroduced.Chapter2exemplify three method, i.e. construction method, Nilpotent-Jacobi methodand nilpotent-centralization method. All of them can prove that sign pattern matrices arespectrally arbitrary.Chapter3presents a special sign pattern matrix and uses Nilpotent-Jacobi method toprove that it is spectrally arbitrary. Moreover, I prove that it is minimal spectrally arbitrary.Chapter4gives another class of special sign pattern matrix and uses Nilpotent-Jacobimethod to prove that it is spectrally arbitrary. Moreover, I prove that it is minimal spectrallyarbitrary, too.