|
|||||
|
|
| 求置换因子循环矩阵的极小多项式和逆的算法 | |
| 引用本文： | 江兆林,徐宗本,高淑萍.求置换因子循环矩阵的极小多项式和逆的算法[J].工程数学学报,2006,23(6):1088-1094. |
| 作者姓名： | 江兆林 徐宗本 高淑萍 |
| 作者单位： | 1. 西安交通大学理学院,西安,710049;临沂师范学院数学系,山东,临沂,276005;曲阜师范大学数学院,山东,曲阜,273165 2. 西安交通大学理学院,西安,710049 3. 西安电子科技大学应用数学系,西安,710071 |
| 基金项目： | Foundation item： 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。 |
| 关 键 词： | 置换因子循环矩阵 极小多项式 公共极小多项式 逆 分块矩阵 Gr(?)bner基 |
| 文章编号： | 1005-3085（2006）06-1088-07 |
| 收稿时间： | 2004-12-31 |
| 修稿时间： | 2004年12月31 |
Algorithms for Finding the Minimal Polynomials and Inverses of Permutation Factor Circulant Matrices |
|
| JIANG Zhao-lin,XU Zong-ben,GAO Shu-ping.Algorithms for Finding the Minimal Polynomials and Inverses of Permutation Factor Circulant Matrices[J].Chinese Journal of Engineering Mathematics,2006,23(6):1088-1094. | |
| Authors: | JIANG Zhao-lin XU Zong-ben GAO Shu-ping |
| Abstract: | In this paper,the permutation factor circulant matrix over any field is introduced.Al- gorithms for computing the minimal polynomial and common minimal polynomial of this kind of matrices over any field are presented by means of the Grbner 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. |
| Keywords: | permutation factor circulant matrix minimal polynomial common minimal polynomial inverse partitioned matrix Gr(?)bner basis |
| 本文献已被 CNKI 维普 万方数据 等数据库收录！ | |