Sign Pattern Matrix Of Inertia

Sign pattern matrix is a very active research topic in combinatorial matrix theory ,the origin ofwhich lies in the study of sign-solvability of linear system. It was ?rst proposed by P.A.Samuelsonin《Foundations of Economic Analysis》,and main results related it before 1995 was summarizedin《Matrices of sign-solvability of linear system》by R.A.Brualdi and B.L.Shader. In our paper, wediscuss the inertia of the Sign pattern matrix. In chapter 1,we introduce the history of developmenton the sign pattern matrices ,some method in our paper had used ,and our research problems andmain results. In chapter 2,we discuss the Spectrally and inertially arbitrary sign pattern, symmetricinertia of nonnegative symmetric sign pattern with zero diagonal ,the development of the conjectureof J.H.Drew et.al, and unique inertia et. In chapter 3,we introduce some methods and problemsrelated the inertia of sign pattern matrix, we also given some problems of not deal with by I known.