Research On Some Cycling Matrix

Quasi circulant matrix is a very important matrix, in this paper, we fours our attention on some properties of three kinds of matrix:r-circulant matrix and left r-circulant matrix、row first plus last right circulant matrix and level-2skew circulant matrix. It consists of four chapters:In chapter one. it has five parts:applications of r-circulant and left r-circulant matrix、row first plus last right circulant matrix and skew circulant matrix in some fields and some properties of those matrix by scholars are introduced in part one, at the same time, the properties of perturbation analysis are mentioned; some defini-tions and rules about r-circulant matrix and row first plus last right circulant matrix are given intensively in part two; we would introduce recurrence relations and Binet formula of ten kinds famous number simultaneously in part three; we provide some important Lemmas in part four; in part five, we introduce what we would do in this paper simply.In chapter two, we discuss some properties of r-circulant and left r-circulant matrix. The chapter consists of two parts. By using the inverse factorization of polynomial of degree n, the explicit determinants of r-circulant and left r-circulant matrices whose first row are six kinds of famous numbers are getted in part one. In part two, consider the definition of norms and the modules of complex number, we obtain the norms of circulant and loft, circulant matrices whose first row arc four kinds famous number skillfully.In chapter three, some base properties of row first plus last right circulant matrix are discussed, such as:eigenvalues, determinant, singularities, rank and so on.In chapter four, based on the style spectral decomposition of base skew circulant matrix and the properties of Kronecker product, we give the block style spectral decomposition of level-2skew circulant matrix directly, and then discuss the optimal backward perturbation analysis for the level-2skew circulant linear system, the supper bounds for the system are given at the same time.