[1]宋海洲.矩阵的最大公因子的结构[J].华侨大学学报(自然科学版),2003,24(3):234-238.[doi:10.3969/j.issn.1000-5013.2003.03.002]
　Song Haizhou.Structure of Greatest Common Divisor of Matrix[J].Journal of Huaqiao University(Natural Science),2003,24(3):234-238.[doi:10.3969/j.issn.1000-5013.2003.03.002]
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矩阵的最大公因子的结构()
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《华侨大学学报（自然科学版）》[ISSN:1000-5013/CN:35-1079/N]

卷:
第24卷
期数:
2003年第3期
页码:
234-238
栏目:
出版日期:
2003-07-20

文章信息/Info

Title:
Structure of Greatest Common Divisor of Matrix
文章编号:
1000-5013(2003)03-0234-05
作者:
宋海洲
华侨大学数学系 福建泉州362011
Author(s):
Song Haizhou
Dept. of Math., Huaqiao Univ., 362011, Quanzhou, China
关键词:
矩阵;  右公因子;  右最大公因子;  行最简形右最大公因子;  行最简形
Keywords:
matrix;  right common divisor;  right greatest common divisor;  right greatest common divisor in row simplest form;  row simplest form
分类号:
O151.21
DOI:
10.3969/j.issn.1000-5013.2003.03.002
文献标志码:
A
摘要:
提出任意两个方阵 A,B的行 (列 )最简形右 (左 )最大公因子的概念 .证明任意两个 n阶方阵A,B的行 (列 )最简形右 (左 )最大公因子的存在唯一性,利用行 (列 )最简形右 (左 )最大公因子给出了 A,B的所有右 (左 )最大公因子构成的集合的表示,给出求它们的简便方法 .最后将其推广至多个矩阵情形 .
Abstract:
The right (left) greatest common divisor in row (column) simplest form as a new concept is offered to arbitrary two square matrices A and B. The unique existence of right ( left) greatest common divisor in row (column) simplest form for arbitrary two square matrices A and B of n order is proved. By applying right (left) greatest common divisor in row (column) simplest form, the representation of the set constructed by all right (left) greatest divisors of A and B can be given, and the simple method for solving them can also be given. The concept is extended to the circumstance of multiple matrices.

参考文献/References:

[1] 张焕玲, 杨昌兰. 矩阵的最大公因子 [J]. 工科数学, 2000(6):93-96.
[2] 同济大学数学教研室. 线性代数 [M]. 北京:高等教育出版社, 2001.1-100.
[3] 张远达. 线性代数原理 [M]. 上海:上海教育出版社, 1981.75-82.

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更新日期/Last Update: 2014-03-23