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Zbl 1159.15006
Wang, Qing-Wen; Song, Guang-Jing; Lin, Chun-Yan
Rank equalities related to the generalized inverse $A^{(2)}_{T,S}$ with applications.
(English)
[J] Appl. Math. Comput. 205, No. 1, 370-382 (2008). ISSN 0096-3003

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 {\it Y.-H. Liu} and {\it M.-S. Wei} [Acta Math. Sin., Engl. Ser. 23, No.~4, 723--730 (2007; Zbl 1123.15003)] and {\it Y. Wang} [SIAM J. Matrix Anal. Appl. 19, No.~2, 407--415 (1998; Zbl 0926.15003)] as some related materials.
MSC 2000:
*15A09 Matrix inversion
15A18 Eigenvalues of matrices, etc.
15A03 Vector spaces

Keywords: rank; linear matrix expression; Moore-Penrose inverse; Drazin inverse; weighted Moore-Penrose inverse; block matrix

Citations: Zbl 1123.15003; Zbl 0926.15003

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