The Eigen-decomposition Of Certain Sign Regular Matrices

Sign regular matrix is a kind of matrix theory with special sign structure ma-trix, its special sign structure is determined by its own signature. The signature of a matrix of tiny difference can cause the its structure and properties of the quite different. This feature determines its have a ratio more extensive theoretical and practical value. For example, in estimating theory, numerical calculation, statistic-s, economics, computer aided geometric design and other aspects. In this paper, we mainly do upper Hessenberg decomposition and eigen-decompositions of certain sign regular matrices with signature (ε1,ε2=ε12,…,εn-1=ε1n-1,εn)-In order to research the effects about the signature and the structure of this kind of sign regular matrix in the process of doing these decomposition.The paper is organized as follows:(1) We briefly introduce the relative background and the present research situ-ation of sign regular matrix. In addition, we introduce the main work of this article.(2) We mainly introduce some definitions, signs and the process of concrete of Neville elimination.(3) We mainly discuss the process of the Neville elimination of the sign regular matrices with signature (ε1,ε2=ε12,…,εn-1=ε1n-1,εn), which preserves the sign structure of this kind of sign regular matrix. And we provide the upper Hessenberg decomposition of sign regular matrix with the same signature.(4) We mainly present the eigen-decomposition of the sign regular matrix with signature ε= (ε1,ε2=ε12,…,εn-1=ε1n-1,εn).