Rank equalities for submatrices in generalized inverse \(M_{T,S}^{(2)}\) of \(M\)

DOI10.1016/S0096-3003(03)00572-1zbMath1054.15002MaRDI QIDQ1826800

Musheng Wei, Yong Hui Liu

Publication date: 6 August 2004

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

zbMATH Keywords

Drazin inverserankMoore-Penrose inversesubmatrixgeneralized inverse \(M^{(2)}_{TS}\)

Mathematics Subject Classification ID

Theory of matrix inversion and generalized inverses (15A09) Vector spaces, linear dependence, rank, lineability (15A03)

Related Items

Rank equalities related to the generalized inverse \(A^{(2)}_{T,S}\) with applications ⋮ The block independence in the generalized inverse \(A_{T,S}(2)\) for some ordered matrices and applications ⋮ Matrix derivatives and Kronecker products for the core and generalized core inverses ⋮ Rank equalities related to the generalized inverses \(A^{\Vert (B_1,C_1)}\), \(D^{\Vert(B_2,C_2)}\) of two matrices \(A\) and \(D\) ⋮ Rank equalities related to a class of outer generalized inverse

Cites Work

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• Nullities of submatrices of the Moore-Penrose inverse
• General expressions for the Moore-Penrose inverse of a 2\(\times 2\) block matrix
• The Moore-Penrose inverse of a partitioned matrix \(M=\begin{pmatrix} D&D\\ B&C\end{pmatrix}\)
• A characterization and representation of the generalized inverse \(A_{T,S}^{(2)}\) and its applications
• Rank equalities related to outer inverses of matrices and applications

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