关于分块置换因子循环矩阵的理论探讨  

Theory of Block Replacement Factor Circulant Matrix

作　　者：陈勇[1] 何承源[1] 凃淑恒 

机构地区：[1]西华大学数学与计算机学院,四川成都610039

出　　处：《昆明理工大学学报（自然科学版）》2011年第4期70-74,共5页Journal of Kunming University of Science and Technology(Natural Science)

基　　金：西华大学应用数学重点学科建设项目(ZXD0910-09-1);西华大学研究生创新基金(Ycjj200913)

摘　　要：提出了块置换因子循环矩阵的概念,并利用Kronecker积和分块多项式定理研究这类矩阵的性质,给出了其行列式的计算方法和可逆的充要条件.当这类矩阵可逆时,它还可以快速地求出其逆阵和以这类矩阵为系数的线性方程组的唯一解.而且这种计算在实数域上是精确的,很容易在计算机上实现.它对于研究这类形式的块状线性方程组有重要的理论意义.The concept of the block replacement factor circulant matrix is presented in this paper. The properties of these matrices are then studied by Kroneeker product and block matrix polynomial theorem. The calculation method of its determinant and necessary and sufficient condition for its inverse are given. When such matrix is invertible, it can quickly calculate the inverse matrix and the only solution of linear equations of using it as the eoefficient. 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.

关 键 词：循环矩阵 置换因子 块 对角化 逆阵 唯一解 

分 类 号：O241[理学—计算数学] O151[理学—数学]