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Rank equalities related to the generalized inverse A T,S (2) with applications. (English) Zbl 1159.15006
The authors establish the rank equalities of some matrix expressions and certain block matrices related to the generalized inverse A T,S (2) . They define the block independence in the generalized inverse A T,S (2) and derive necessary and sufficient conditions for two, three and four ordered matrices to be independent in A T,S (2) , respectively. As special cases, they present the corresponding results on the weighted Moore-Penrose inverse and the Drazin inverse. See Y.-H. Liu and M.-S. Wei [Acta Math. Sin., Engl. Ser. 23, No. 4, 723–730 (2007; Zbl 1123.15003)] and Y. Wang [SIAM J. Matrix Anal. Appl. 19, No. 2, 407–415 (1998; Zbl 0926.15003)] as some related materials.
MSC:
15A09Matrix inversion, generalized inverses
15A18Eigenvalues, singular values, and eigenvectors
15A03Vector spaces, linear dependence, rank