Some identities for Moore–Penrose inverses of matrix products

DOI10.1080/03081080410001699334zbMath1070.15003OpenAlexW2057498274MaRDI QIDQ4655432

Shizhen Cheng, Yongge Tian

Publication date: 11 March 2005

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

Full work available at URL: https://doi.org/10.1080/03081080410001699334

zbMATH Keywords

matrix productDrazin inverseweighted Moore-Penrose inversereverse order lawmatrix identity

Mathematics Subject Classification ID

Theory of matrix inversion and generalized inverses (15A09) Matrix equations and identities (15A24)

Related Items (15)

Miscellaneous reverse order laws and their equivalent facts for generalized inverses of a triple matrix product ⋮ On the product of projectors and generalized inverses ⋮ Two groups of mixed reverse order laws for generalized inverses of two and three matrix products ⋮ Pseudoinverses of Signed Laplacian Matrices ⋮ Miscellaneous reverse order laws for generalized inverses of matrix products with applications ⋮ Identities concerning the reverse order law for the Moore-Penrose inverse ⋮ New identities for Moore-Penrose inverses of some operator products and their reverse-order laws ⋮ Reverse order law in \(C^{\ast }\)-algebras ⋮ Unnamed Item ⋮ Estimating covariance and precision matrices along subspaces ⋮ Weighted Moore-Penrose inverses of arbitrary-order tensors ⋮ The equivalence between (AB)^†=B^†A^†and other mixed-type reverse-order laws ⋮ Some mixed-type reverse-order laws for the Moore-Penrose inverse of a triple matrix product ⋮ Improved multivariate normal mean estimation with unknown covariance when \(p\) is greater than \(n\) ⋮ Unnamed Item

Cites Work

• The reverse order law revisited
• The product of operators with closed range and an extension of the reverse order law
• Reverse order laws for the generalized inverses of multiple matrix products
• Using rank formulas to characterize equalities for Moore-Penrose inverses of matrix products.
• An Extension of the Generalized Inverse of a Matrix
• The equivalence between (AB)^†=B^†A^†and other mixed-type reverse-order laws

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