3个复矩阵若干广义逆的结构表达式及其块独立性

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．

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

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 theory,measurement,statistics and econometrics.The progress of technology ushered in the information era,and the research of bordered matrices and its generalized inverses becomes more and more important.In this paper,we obtain the structures of the generalized 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.