The equivalence between (AB)†=B†A†and other mixed-type reverse-order laws

DOI10.1080/00207390500226168zbMath1274.15019OpenAlexW2064830189MaRDI QIDQ5716526

Yongge Tian

Publication date: 2006

Published in: International Journal of Mathematical Education in Science and Technology (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00207390500226168

Mathematics Subject Classification ID

Theory of matrix inversion and generalized inverses (15A09)

Related Items (17)

Basic reverse order law and its equivalencies ⋮ Miscellaneous reverse order laws and their equivalent facts for generalized inverses of a triple matrix product ⋮ Two groups of mixed reverse order laws for generalized inverses of two and three matrix products ⋮ Miscellaneous reverse order laws for generalized inverses of matrix products with applications ⋮ Reverse order law in \(C^{\ast }\)-algebras ⋮ Mixed-type reverse-order laws for \(\{1, 3, 4\}\)-generalized inverses over Hilbert spaces ⋮ Some results on the reverse order law in rings with involution ⋮ Further results on the reverse order law for the Moore-Penrose inverse in rings with involution ⋮ Reverse order laws for the generalized strong Drazin inverses ⋮ Some identities for Moore–Penrose inverses of matrix products ⋮ Equalities for orthogonal projectors and their operations ⋮ Equalities and inequalities for ranks of products of generalized inverses of two matrices and their applications ⋮ A CANCELLATION PROPERTY OF THE MOORE–PENROSE INVERSE OF TRIPLE PRODUCTS ⋮ Equivalence analysis of different reverse order laws for generalized inverses of a matrix product ⋮ A study of range equalities for mixed products of two matrices and their generalized inverses ⋮ Reverse order laws for Hirano inverses in rings ⋮ Further results on the Moore–Penrose invertibility of projectors and its applications

Cites Work

• On pseudoinverses of operator products
• The product of operators with closed range and an extension of the reverse order law
• Using rank formulas to characterize equalities for Moore-Penrose inverses of matrix products.
• On mixed-type reverse-order laws for the Moore-Penrose inverse of a matrix product
• Rank equalities related to outer inverses of matrices and applications
• Some identities for Moore–Penrose inverses of matrix products
• Note on the Generalized Inverse of a Matrix Product
• An Extension of the Generalized Inverse of a Matrix

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