任意除环上一矩阵方程组的一般解与中心和反中心对称解

数学季刊 ›› 2006, Vol. 21 ›› Issue (1): 66-70.

任意除环上一矩阵方程组的一般解与中心和反中心对称解

Department of Information and Computer Science, Zhengzhou Light Industry Institute, Zhengzhou 450002, China;School of Mathematics and Information, Business Administration University of Shandong, Yantai 264005, China

收稿日期:2004-03-14 出版日期:2006-03-30 发布日期:2023-12-21
作者简介:QIN Jian-guo(1957-),male,native of Tangyin,Henan,an associate professor of Zhengzhou Light Industry Institute,engages in matrix theory;SONG Guang-ai(1963-),male,native of Weifang,Shandong, an associate professor of Business Administration University of Shandong,Ph.D.,engages in Lee algebra.
基金资助:
Supported by the National Natural Science Foundation of China(10471085)；

The General and Centro(Kewsy) Symmetric Solutions to a System of Matrix Equations over an Arbitrary Skew Field

Department of Information and Computer Science, Zhengzhou Light Industry Institute, Zhengzhou 450002, China;School of Mathematics and Information, Business Administration University of Shandong, Yantai 264005, China

Received:2004-03-14 Online:2006-03-30 Published:2023-12-21
About author:QIN Jian-guo(1957-),male,native of Tangyin,Henan,an associate professor of Zhengzhou Light Industry Institute,engages in matrix theory;SONG Guang-ai(1963-),male,native of Weifang,Shandong, an associate professor of Business Administration University of Shandong,Ph.D.,engages in Lee algebra.
Supported by:
Supported by the National Natural Science Foundation of China(10471085)；

摘要/Abstract

摘要： Necessary and sufficient conditions are given for the existence of the general solution, the centrosymmetric solution, and the centroskewsymmetric solution to a system of linear matrix equations over an arbitrary skew field. The representations of such the solutions of the system are also derived.

关键词: system of matrix equations, inner inverse of a matrix, reflexive inverse of a
matrix, centro(skew)symmetric , matrix, skew , field

Abstract: Necessary and sufficient conditions are given for the existence of the general solution, the centrosymmetric solution, and the centroskewsymmetric solution to a system of linear matrix equations over an arbitrary skew field. The representations of such the solutions of the system are also derived.

Key words: system of matrix equations, inner inverse of a matrix, reflexive inverse of a
matrix, centro(skew)symmetric , matrix, skew , field

中图分类号:

O151.21

秦建国, 宋光艾. 任意除环上一矩阵方程组的一般解与中心和反中心对称解[J]. 数学季刊, 2006, 21(1): 66-70.

QIN Jian-guo, SONG Guang-ai . The General and Centro(Kewsy) Symmetric Solutions to a System of Matrix Equations over an Arbitrary Skew Field[J]. Chinese Quarterly Journal of Mathematics, 2006, 21(1): 66-70.

[1]	季琳星, 张科, 胡文军. 单层圆柱形网格图的独立多项式和Merrifield-Simmons指数[J]. 数学季刊, 2024, 39(4): 379-387.
[2]	攸晓杰, 马海成, 张斌, 李雅兰. 两类四圈图的奇异性[J]. 数学季刊, 2023, 38(4): 349-359.
[3]	曾敏, 袁永新. 一个2×2块矩阵的Moore-Penrose逆的显式公式[J]. 数学季刊, 2023, 38(4): 401-409.
[4]	董昌州, 李浩雪. 矩阵方程的最小二乘{P,Q,k+1}-自反解[J]. 数学季刊, 2023, 38(2): 210-220.
[5]	黄卓红. 奇异鞍点问题中广义位移分裂迭代方法的半收敛性分析[J]. 数学季刊, 2023, 38(2): 145-156.
[6]	靳正芬, 王朵, 尚有林, 律金曼. 一种求解未知噪音水平的低秩矩阵恢复问题有效算法 [J]. 数学季刊, 2021, 36(4): 356-368.
[7]	张士君, 王世恒, 王珂. 耦合Lyapunov 矩阵方程的AOR迭代法[J]. 数学季刊, 2021, 36(2): 141-148.
[8]	龙兵, 张忠占. 区间删失下恒定应力部分加速寿命试验的统计分析[J]. 数学季刊, 2019, 34(1): 1-13.
[9]	曹南斌, 张玉平. 矩阵方程组AX=C;XB=D{P;k+1}-反射解的研究[J]. 数学季刊, 2018, 33(1): 32-42.
[10]	陈爱敏, 刘发旺. 有限体积方法非结构网格方法解分数阶Allen-Cahn程[J]. 数学季刊, 2017, 32(4): 345-354.
[11]	杜法鹏. 2×2分块矩阵群逆的表示[J]. 数学季刊, 2016, 31(4): 412-421.
[12]	杨若松, 王力工. 具有s=5,6的距离整完全多部图[J]. 数学季刊, 2016, 31(2): 111-117.
[13]	张景丽, 汤平, 马松雅. 一种有效的安全网络编码构造[J]. 数学季刊, 2016, 31(1): 60-68.
[14]	张劲松. 判定广义严格对角占优矩阵的新准则[J]. 数学季刊, 2015, 30(2): 166-171.
[15]	程媛媛, 蒋威. 含两个不同时变时滞连续系统的稳定性判据[J]. 数学季刊, 2015, 30(1): 30-38.