On some matrix equalities for generalized inverses with applications

DOI10.1016/j.laa.2008.12.005zbMath1165.15006OpenAlexW2003785292MaRDI QIDQ1017632

George P. H. Styan, Yongge Tian

Publication date: 12 May 2009

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2008.12.005

zbMATH Keywords

Schur complementgeneralized inverseadditive decompositionblock decompositionmatrix equalitymatrix rank methodparallel sum of matricesshorted matrix

Mathematics Subject Classification ID

Theory of matrix inversion and generalized inverses (15A09) Matrix equations and identities (15A24) Vector spaces, linear dependence, rank, lineability (15A03)

Related Items (4)

On additive decompositions of solutions of the matrix equation \(AXB=C\) ⋮ On additive decomposition of the Hermitian solution of the matrix equation \(AXA^* = B\) ⋮ Professor Haruo Yanai and multivariate analysis ⋮ Classification analysis to the equalities A^(i,…,j) = B^(k,…,l) for generalized inverses of two matrices

Cites Work

• On parallel sum and difference of matrices
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• On parallel summability of matrices
• The Moore-Penrose inverses of \(m\times n\) block matrices and their applications
• Schur complements and statistics
• Shorted matrices - an extended concept and some applications
• The regular shorted matrix and the hybrid sum
• The nonunique parallel sum
• The dimension of intersection of \(k\) subspaces
• How to express a parallel sum of \(k\) matrices
• A generalization of parallel addition
• Upper and lower bounds for ranks of matrix expressions using generalized inverses
• Generalized inverses. Theory and applications.
• A note on the generalized rank reduction
• Invariance properties of a triple matrix product involving generalized inverses
• Series and parallel addition of matrices
• On the Wedderburn-Guttman theorem
• A remark on the characterization of the parallel sum of two matrices
• The Moore–Penrose inverse for sums of matrices under rank additivity conditions
• The Moore--Penrose Generalized Inverse for Sums of Matrices
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