The Theory Of Generalized Permutation Circulant Matrix

Special matrix type of research is an important part of matrix theory, and applied mathematics is increasingly becoming a very active and important research direction. Since such matrix there are many good nature and structure, it is necessary to promote its. The article in the previous cycle of the permutation matrix of factors, based on its further promotion, and to explore the special nature of the algorithm. Mainly includes the following:1,The concept of r-permutation matrix and block replacement matrix are proposed in connection with the problem of permutation matrices in orthogonal and permutation group and its characters are studied.Moreover,the algorithm of such inverse matrix and the necessary and sufficient conditions of determine one square is r-permutation matrix are obtained use of Hadamard product.All these are extremely important for our research and extension permutation matrix.2, r-permutation factor circulant matrix is defined and its nature are studied.First,the determined conditions of the inverse and generalized inverse of these matrices have been found,in which matrix inverse and generalized inverse are still the r-permutation factor circulant matrices.Moreover,the paper has gaven the algorithm of the inverse and generalized inverse of matrix.。Second, a fast algorithm for conditions of solution and solution of r-permutation factor circulant matrix equation AX = b are presented.When r-permutation factor circulant matrix are nonsingular,it computes the single solution of r-permutation factor circulant matrix equation; When r-permutation factor circulant matrix are singular, it computes the special solution and general of r-permutation factor circulant matrix equation.3,The paper presents a concept of the block replacement factor circulant matrix and studies the nature of these matrices use of Kronecker product and sub-block matrix polynomial theorem.The calculation method of its determinant and reversible necessary and sufficient condition are given. When such matrix invertible, it can quickly calculate the inverse matrix and the only solution of linear equations of using it as the coefficient.Moreover, the calculation in the real number field is accurate and it is easy to implement on the computer. It has important theoretical significance for study of these block linear equations.