Study On Some Problems Of The Circular Matrix

Circulant matrices become important research contents of the matrix theory for their wide application domain. And Circulant matrices are increasingly becoming one of the active research directions in applied mathematics and computational mathematics. The research on the solution for the inverse matrices of special circulant matrix has been a hot issue in recent years. However, the research on r-block permutation factor circulant matrix is quite rare. The research on special circulant matrix contains important practical significance for its excellent structure and property, important application in technology project. The present paper will mainly research Level-2(r1,r2)-circulant matrices of type (m,n) and r-block permutation factor circulant matrix and the findings are as follows:1. For level-2(r1, r2)-circulant matrices of type (m, n), the formula of its inverse matrix is given by the Kronecker product if A is nonsingular. A generalized inverse of A will be the constructed by Kronecker product if A is singular. In particular, the method can be used to seek Moor-penrose inverse of a singular Level-2circulant matrices of type(m, n).2. r-block permutation factor circulant matrix is defined and its property are studied. Diagonalization, eigenvalue and the formula on its inverse matrix are reached by Kronecker. Similarly, Kronecker and Fourier matrix are utilized to construct eigenvector matrix of r-block permutation factor circulant matrix. And then spectral decomposition methods of r-block permutation factor circulant matrix are reached.