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| 矩阵乘积关于广义逆的交换律及广义交换律 | |
| 引用本文： | 李莹,高岩,郭文彬.矩阵乘积关于广义逆的交换律及广义交换律[J].上海理工大学学报,2011,33(4). |
| 作者姓名： | 李莹 高岩 郭文彬 |
| 作者单位： | 1. 上海理工大学管理学院,上海200093;聊城大学数学科学学院,聊城252059 2. 上海理工大学管理学院,上海,200093 3. 聊城大学数学科学学院,聊城,252059 |
| 基金项目： | 国家自然科学基金资助项目(11171221) |
| 摘 要： | 定义了两个矩阵乘积关于广义逆的交换律与广义交换律的概念,利用矩阵秩方法及奇异值分解分别研究了两个矩阵乘积关于{1}-逆,{1,2}-逆,{1,3}-逆与{1,4}-逆的交换律与广义交换律成立的充要条件,并对其进行了比较. |
| 关 键 词： | {i j k}-逆 群逆 广义Schur补 秩方法 奇异值分解 交换律 |
Commutative law and generalized commutative law of matrix multiplication on generalized inverse |
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| LI Ying,GAO Yan and GUO Wen bin.Commutative law and generalized commutative law of matrix multiplication on generalized inverse[J].Journal of University of Shanghai For Science and Technology,2011,33(4). | |
| Authors: | LI Ying GAO Yan and GUO Wen bin |
| Institution: | LI Ying1,2,GAO Yan1,GUO Wen-bin2(1.Business School,University of Shanghai for Science and Technology,Shanghai 200093,China,2.College of Mathematics Science,Liaocheng University,Liaocheng 252059,China) |
| Abstract: | The concepts of the commutative laws and generalized commutative laws of matrix multiplication on generalized inverse were defined.Using the matrix rank method and SVD,necessary and sufficient conditions about the commutative laws and generalized commutative laws of matrix multiplication on {1}-inverse,{1,2}-inverse,{1,3}-inverse and {1,4}-inverse were established respectively,and these conditions were compared between themselves. |
| Keywords: | {i j k}-inverse group inverse generalized Schur complement matrix rank method singular value decomposition commutative laws |
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