The Inertia Characterization Of The Approximate Symbol Mode

Sign pattern matrix is an important branch of combinatorial matrix theory.The theory of sign pattern matrix mainly studies the combinatorial properties of qualitative matrix determined by sign pattern matrices.It has wide application in many subjects,such as combinatorial matrix theory,graph theory matrix analysis,ordinary differential equations and algorithm theory.R.A.Brualdi and B.L.Shader summarized the results obtained by the year 1995 in the book of ?Matrices of Sign-solvable Linear Systems?.This book lay a solid foundation for later development and push the topic research to a new height.Since then a large number of research articles about sign pattern matrix are emerged and many new concepts are produced such as the complex patterns,ray patterns,etc.In this paper,we mainly characterize a class of inertially arbitrary reducible sign pattern.Chapter 1 provides an overview of research history of sign pattern matrix,introduce some basic knowledge,and the work of this paper is put forward.Chapter 2 introduces several kinds of important properties of matrix's inertia and dynamic study of inertia.Chapter 3 describes a special kind of inertially arbitrary sign patterns,namely reducible inertia arbitrary sign patterns.And fully characterize the reducible inertially arbitrary sign patterns of orders 4,5 and 6.