| 一对四元数矩阵方程的共轭延拓解 |
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| 引用本文： | 聂祥荣,;王卿文.一对四元数矩阵方程的共轭延拓解[J].应用数学与计算数学学报,2014(4):440-448. |
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| 作者姓名： | 聂祥荣 ;王卿文 |
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| 作者单位： | [1]上海大学理学院,上海200444; [2]毕节学院数学系,贵州毕节551700 |
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| 基金项目： | 国家自然科学基金资助项目（11171205）;贵州省科学技术基金资助项目（LKB[2013]11） |
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| 摘 要： | 定义广义四元数共轭延拓矩阵的概念,利用矩阵分块和四元数矩阵的实表示方法,分别给出四元数矩阵方程AX=C和XB=D存在列共轭延拓解和行共轭延拓解的必要充分条件及解的表达式.
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| 关 键 词： | 四元数矩阵 矩阵方程 共轭延拓矩阵 实表示 |
Conjugated extended matrix solutions to a pair of quaternion matrix equations |
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| Institution: | NIE Xiang-rong,WANG Qing-wen(1. College of Sciences, Shanghai University, Shanghai 200444, China; 2. Department of Mathematics, Bijie University, Bijie 551700, Guizhou Province, China) |
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| Abstract: | The conjugated extended quaternion matrix is defined in this paper.By introducing real representations of quaternion matrices,we give the necessary and sufficient conditions for the existence of column and row conjugated extended solutions to quaternion matrix equations AX = C and YB = C as well as the representations of such solutions,respectively,when the consistency conditions are met. |
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| Keywords: | quaternion matrix matrix equation conjugated extended matrix real representation |
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