求置换因子循环矩阵的极小多项式和逆的算法(英文)  

Algorithms for Finding the Minimal Polynomials and Inverses of Permutation Factor Circulant Matrices

作　　者：江兆林[1] 徐宗木 高淑萍[2] 

机构地区：[1]西安交通大学理学院 [2]西安电子科技大学应用数学系,西安710071

出　　处：《工程数学学报》2006年第6期1088-1094,共7页Chinese Journal of Engineering Mathematics

基　　金：The 35th Postdoctoral Work Science Foundation of China(2004035684)

摘　　要：本文引入了任意域上置换因子循环矩阵,利用多项式环的理想的Gr(?)bner基的算法给出了任意域上置换因子循环矩阵的极小多项式和公共极小多项式的算法,同时给出了这类矩阵逆矩阵的两种算法最后,利用Schur补给出了任意域上具有置换因子循环矩阵块的分块矩阵逆的一个算法,在有理数域或模素数剩余类域上,这一算法可由代数系统软件CoCoA4．0实现。In this paper, the permutation factor circulant matrix over any field is introduced. Algorithms for computing the minimal polynomial and common minimal polynomial of this kind of matrices over any field are presented by means of the Groebner basis of the ideal in the polynomial ring, and two algorithms for finding the inverses of such matrices are also presented. Finally, an algorithm for the inverse of partitioned matrix with permutation factor circulant blocks over any field is given by using the Schur complement, which can be implemented by CoCoA 4.0, an algebraic system, over the field of rational numbers or the field of residue classes of modulo prime number.

关 键 词：置换网子循环矩阵 极小多项式 公共极小多项式 逆 分块矩阵 GROEBNER基 

分 类 号：O151.2[理学—数学]