Study On Block Skew-Symmetric And Skew-Circulant Matrix

The research of circulant matrix is an important part of matrix theory, and the matrix has become a very active and important research direction in applied mathematics. Block skew-symmetric and skew–circulant matrix plays an important part in circulant matrix field, it is necessary for us to promote it and study its special characteristics , due to the good nature and structure of the matrix. This paper is based on the research of Liu Xuejie on the characteristics of the skew- symmetric and skew-circulant matrix. We give the solution of the inverse, generalized inverse, eigenvalues and determinant of the skew- symmetric and skew-circulant matrix, also the paper discuses the anti-problem and the solution of Linear Equations. The research objects focus on the eigenvalues of block skew-symmetric and skew-circulant matrix whose sub-block are symmetric matrix, symmetric skew circulation, skew-symmetric and skew–circulant matrix respectively and the solution of the inverse of block skew-symmetric and skew-circulant matrix.This paper contains the following three parts:First: it gives the relevant background knowledge, the main ideas contain the study of circulant matrices at home and abroad, the basic concepts, characteristics of circulant matrices, and the basic computing instruments which have been frequently used in matrix theory and matrix calculations.Second: in this paper, we give a series of the characteristics of skew-symmetric and skew-circulant matrix. Then we give the method of solving the inverse and generalized inverse of the skew- symmetric and skew-circulant matrix, the method of solving the eigenvalues and determinant of the matrix, and have studied its anti-problem and computed the solution of the linear equation.Third: we give the eigenvalues of block skew-symmetric and skew-circulant matrix whose sub-block are symmetric matrix, symmetric skew circulation, skew-symmetric and skew–circulant matrix, and study the inverse matrix of this kind of matrix.