Moore–Penrose invertibility in involutory rings: the case aa †=bb †

DOI10.1080/03081080802652279zbMath1193.15002OpenAlexW2093676386MaRDI QIDQ3564207

Pedro Patrício, C. Mendes Araújo

Publication date: 2 June 2010

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

Full work available at URL: https://doi.org/10.1080/03081080802652279

zbMATH Keywords

Moore-Penrose inverse\(\ast \)-regular rings

Mathematics Subject Classification ID

Theory of matrix inversion and generalized inverses (15A09) Rings with involution; Lie, Jordan and other nonassociative structures (16W10) Conditions on elements (16U99)

Related Items (23)

*-DMP elements in *-semigroups and *-rings ⋮ A new class of generalized inverses in semigroups and rings with involution ⋮ Weighted binary relations involving the Drazin inverse ⋮ Suitable elements, -clean elements and Sylvester equations in rings with involution ⋮ Projections for generalized inverses ⋮ Weighted G-Drazin inverses and a new pre-order on rectangular matrices ⋮ Expansion formulas for the inertias of Hermitian matrix polynomials and matrix pencils of orthogonal projectors ⋮ A simultaneous canonical form of a pair of matrices and applications involving the weighted Moore-Penrose inverse ⋮ One-sided w-core inverses in rings with an involution ⋮ Reverse order law for the inverse along an element ⋮ Left \(w\)-core inverses in rings with involution ⋮ The Moore-Penrose inverse of a companion matrix ⋮ The inverse along a lower triangular matrix ⋮ On the covariance of Moore-Penrose inverses in rings with involution ⋮ On some new pre-orders defined by weighted Drazin inverses ⋮ Centralizer's applications to the inverse along an element ⋮ Characterizations of core and dual core inverses in rings with involution ⋮ Several characterizations for generalized inverses in a ring ⋮ On a revisited Moore-Penrose inverse of a linear operator on Hilbert spaces ⋮ The diamond partial order in rings ⋮ The core invertibility of a companion matrix and a Hankel matrix ⋮ Projections generated by Moore–Penrose inverses and core inverses ⋮ Idempotents generated by weighted generalized inverses in rings with involution

Cites Work

• Moore-Penrose inverse in rings with involution
• On some characterizations of the star partial ordering for matrices and rank subtractivity
• The Moore-Penrose inverse of a morphism with factorization
• Block generalized inverses
• The Moore-Penrose inverse of a factorization
• Generalized invertibility in two semigroups of a ring.
• Perturbation of the Drazin inverse for matrices with equal eigenprojections at zero
• Elements of rings with equal spectral idempotents
• The Moore-Penrose inverse of von Neumann regular matrices over a ring

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