求鳞状循环因子矩阵的极小多项式的算法(英文)  

An algorithm for Finding the Minimal Polynomial of a Scaled Circulant Factor Matrix

作　　者：江兆林[1] 刘三阳[1] 

机构地区：[1]山东临沂师范学院数学系

出　　处：《应用数学》2004年第1期61-66,共6页Mathematica Applicata

基　　金：SupportedbytheNationalNaturalScienceFoundationofChina (6 9972 0 36 )

摘　　要：提出了任意域上鳞状循环因子矩阵 ,利用多项式环的理想的Go bner基的算法给出了任意域上鳞状循环因子矩阵的极小多项式和公共极小多项式的一种算法 .同时给出了这类矩阵逆矩阵的一种求法 .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Co CoA4 .0实现 .In this paper,the scaled circulant factor 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 algorithm for the Grbner basis of the ideal in the polynomial ring,and an algorithm for finding the inverse of such matrices are also presented,which can be realized by CoCoA 4.0,an algebraic system,over the field of rational numbers or the field of residue classes of modulo prime number.Numerical examples show the effectiveness of the algorithms.

关 键 词：鳞状循环因子矩阵 极小多项式 多项式环 逆矩阵 

分 类 号：O151.21[理学—数学] O153.3[理学—基础数学]