3个复矩阵若干广义逆的结构表达式及其块独立性  

On the block independency of three matrices and the structural representation for the generalized inverses of two matrices

作　　者：韩秀平[1] 魏木生[1] 

机构地区：[1]上海师范大学数理学院,上海200234

出　　处：《上海师范大学学报（自然科学版）》2012年第1期12-30,共19页Journal of Shanghai Normal University(Natural Sciences)

基　　金：国家自然科学基金资助项目(10771073);上海市重点学科基金资助项目(S30405)

摘　　要：加边矩阵及其广义逆是数学的一个重要分支,具有极为丰富的内容.作为一种基本的工具,加边矩阵及其广义逆在数学学科以及其他科学技术领域,如控制论、系统辨识、规划论、网络理论、测量、统计和计量经济学等方面都有着十分重要的应用.因此,学习和掌握加边矩阵及其广义逆的基本理论方法是必不可少的.而且随着科技的进步,人类开始步入信息化、数字化时代,加边矩阵及其广义逆在生产实践中的应用越来越广泛,加边矩阵及其广义逆的研究也越来越重要.应用QQ-SVD分解,得到了3个矩阵广义逆的结构形式,并且给出了3个矩阵块独立性的充要条件.Bordered matrices and their generalized inverses is an important and rich branch of mathematics. As a basic tool, it is widely applied to mathematics and other fields of science,like control theory, system identification, planning theory, network the- ory, measurement, statistics and econometrics. The progress of technology ushered in the information era, and the research of bor- dered matrices and its generalized inverses becomes more and more important. In this paper, we obtain the structures of the gener- alized inverses of three matrices by applying the restricted singular value decomposition QQ - SVD, and present a necessary and sufficient condition for the block independency of three matrices.

关 键 词：块独立 G-逆 QQ-SVD 

分 类 号：O177.5[理学—数学]