Tian, Yongge Rank equalities for block matrices and their Moore-Penrose inverses. (English) Zbl 1057.15006 Houston J. Math. 30, No. 2, 483-510 (2004). The author considers: a) the relationship between \(\left[ \begin{smallmatrix} A\\ B \end{smallmatrix} \right] \) and \(\left[ \begin{smallmatrix} A^{† } \\ B^{† } \end{smallmatrix} \right] \), where \(A^{† }\) denotes the Moore-Penrose inverse of \(A\), through some rank equalities, and b) a variety of rank equalities for \( 2\times 2\) block matrices and their Moore-Penrose inverses, that can easily characterize equalities for Moore-Penrose inverses of block matrices. Reviewer: Nicholas Karampetakis (Thessaloniki) Cited in 13 Documents MSC: 15A09 Theory of matrix inversion and generalized inverses 15A24 Matrix equations and identities 15A03 Vector spaces, linear dependence, rank, lineability Keywords:block matrix; Moore-Penrose inverse; outer inverse; generalized inverse; range; rank; rank equalities PDFBibTeX XMLCite \textit{Y. Tian}, Houston J. Math. 30, No. 2, 483--510 (2004; Zbl 1057.15006)