循环矩阵分解的算子方法  

Operator method for the factorization of circulant matrices

作　　者：黄潇[1] 吴化璋[1] 

机构地区：[1]合肥工业大学数学学院,安徽合肥230009

出　　处：《合肥工业大学学报（自然科学版）》2012年第5期704-707,共4页Journal of Hefei University of Technology：Natural Science

基　　金：安徽省自然科学基金资助项目(1208085MA02)

摘　　要：文章通过位移算子方法研究循环矩阵,首先从循环矩阵与Toeplitz矩阵的关系出发,给出有理函数生成的循环矩阵的概念,得到循环矩阵的Vandermonde分解形式;其次,由循环矩阵与Toeplitz-Bezout矩阵的关系给出循环矩阵的另一种位移算子表示,并证明了循环矩阵满足Barnett分解公式。In this paper,the shift operator method is applied to studying the circulant matrices.First,in view of the relation between circulant matrices and Toeplitz matrices,the concept of circulant matrices generated by rational functions is introduced and the Vandermonde factorization form of circulant matrices is obtained.Second,according to the relation between circulant matrices and Toeplitz-Bezout matrices,another type of the representation of circulant matrices with the shift operator is gotten,and the Barnett＇s factorization formula for circulant matrices is also verified.

关 键 词：TOEPLITZ矩阵 Toeplitz-Bezout矩阵 循环矩阵 位移算子 

分 类 号：O151.21[理学—数学]