中心代数上一矩阵方程的中心对称与中心斜对称解

数学季刊 ›› 2003, Vol. 18 ›› Issue (2): 111-116.

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中心代数上一矩阵方程的中心对称与中心斜对称解

Department of Mathematics, University of Science and Technology of China , Hefei 230026, China; Department of Mathematics, University of Yangzhou , Yangzhou 225002, China

收稿日期:2000-06-12 出版日期:2003-06-30 发布日期:2024-04-12
作者简介:WANG Qing-wen(1964-),male,native of Weifang,Shandong,a professor of University of Science and Technology of China,Ph.D.,engages in matrix theory and group theory.
基金资助:
Supported by the Natural Science Foundation of China(10071078)； Supported by the Natural Science Foundation of Shandong Province(Q99A08)；

On the Centrosymmetric and Centroskewsymmetric Solutions to a Matrix Equation over a Central Algebra

Department of Mathematics, University of Science and Technology of China , Hefei 230026, China; Department of Mathematics, University of Yangzhou , Yangzhou 225002, China

Received:2000-06-12 Online:2003-06-30 Published:2024-04-12
About author:WANG Qing-wen(1964-),male,native of Weifang,Shandong,a professor of University of Science and Technology of China,Ph.D.,engages in matrix theory and group theory.
Supported by:
Supported by the Natural Science Foundation of China(10071078)； Supported by the Natural Science Foundation of Shandong Province(Q99A08)；

摘要/Abstract

摘要： Let Ω be a finite dimensional central algebra and chart Ω≠2. The matrix equation AXB - CXD = E over Ω is considered. Necessary and sufficient conditions for the existence of centro(skew)symmetric solutions of the matrix equation are given. As a particular case, the matrix equation X - AXB = C over Ω is also considered.

关键词: central , , algebra, matrix , , equation, centro(skew)symmetric , , matrix, regular , , matrix , , quadruple ,

Abstract: Let Ω be a finite dimensional central algebra and chart Ω≠2. The matrix equation AXB - CXD = E over Ω is considered. Necessary and sufficient conditions for the existence of centro(skew)symmetric solutions of the matrix equation are given. As a particular case, the matrix equation X - AXB = C over Ω is also considered.

Key words: central , , algebra, matrix , , equation, centro(skew)symmetric , , matrix, regular , , matrix , , quadruple

中图分类号:

O151.21

王卿文, 孙建华, 李尚志. 中心代数上一矩阵方程的中心对称与中心斜对称解[J]. 数学季刊, 2003, 18(2): 111-116.

WANG Qing-wen , SUN Jian-hua, LI Shang-zhi. On the Centrosymmetric and Centroskewsymmetric Solutions to a Matrix Equation over a Central Algebra[J]. Chinese Quarterly Journal of Mathematics, 2003, 18(2): 111-116.

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中心代数上一矩阵方程的中心对称与中心斜对称解

On the Centrosymmetric and Centroskewsymmetric Solutions to a Matrix Equation over a Central Algebra

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