r-块置换因子循环矩阵及其逆矩阵的求法  

r-BlockPermutation Factor Circulant Matrix and Inverse Matrix

作　　者：胡艳[1] 秦克云[1] 孙继忠[2] 

机构地区：[1]西南交通大学数学学院,成都610031 [2]中兴通讯股份有限公司,西安710065

出　　处：《重庆师范大学学报（自然科学版）》2012年第4期63-67,共5页Journal of Chongqing Normal University:Natural Science

基　　金：国家自然科学基金(No.61175055)

摘　　要：给出了r-块置换因子循环矩阵的定义,借助于Kronecker积讨论了r-块置换因子循环矩阵的基本性质,并证明了r-块置换因子循环矩阵具有可交换性,即AB=BA。然后在r-块置换因子循环矩阵对角化的基础上给出了其行列式的计算方法以及非奇异矩阵的充要条件。最后,给出了非奇异的r-块置换因子循环矩阵的逆矩阵求法。The concept of r-block permutation factor circulant matrix is presented. The characteristics of r-block permutation factor circulant matrix are discussed by Kronecker. The interchange ability of r-block permutation factor circulant matrix has been demonstrated, that is AB= BA. The calculation method of matrix determinant and the sufficient condition of nonsingular matrix based on the diagonalization of circulant matrices are given. Finally, the method of inverse matrix is given in r-block permutation factor eirculant matrix.

关 键 词：r-块置换因子循环矩阵 非奇异性 对角化 逆矩阵 块 

分 类 号：O241[理学—计算数学]