On The Block Independency Of Three Matrices And The Structural Representation For The Generalized Inverses Of Three Matirces

Bordered matrices and their generalized inverses are an important topic of matrices analysis.Bordered matrices and their generalized inverses are widely used in mathematics and otherfields of science, like control theory, system identification, planning theory, network theory,measurement, statistics and econometrics. Therefore, it is essential for us to learn and master thebasic methods for the bordered matrices and their generalized inverses. And with the progressof technology, the human being has been ushered in the information era, bordered matrices andtheir generalized inverses are widely used to solve problem in practice, also, the research ofbordered matrices and their generalized inverses become more and more important.In this article, we obtain the structures of the generalized inverses of three matrices by ap-plying the doubly quotient singular value decomposition QQ-SVD, and present necessary andsufficient conditions for block independency of three matrices.The contents of this thesis are divided into three parts.1. The structures of {1,2,3}-inverses and {1,3,4}-inverses of {C, A, B} and M based onthe QQ-SVD of {C,A,B}We derive the structures of {1,2,3}-inverses and {1,3,4}-inverses of A, B, C and M, based on theQQ-SVD of {C,A,B}.2. Under the definition1.3.2, the block independence of matrices {C, A, B} with respectto {1,2,3}-inverses and {1,3,4}-inversesBased on the structures of {1,2,3}-inverses and {1,3,4}-inverses of {C, A, B}, we obtain the blockindependence under the definition1.3.2.3. Under the definition1.3.3, the block independence of matrices {C, A, B} with respectto {1,2,3}-inverses and {1,3,4}-inversesBased on the structures of {1,2,3}-inverses and {1,3,4}-inverses of {C, A, B}, we obtain the blockindependence under the definition1.3.3.