Group, Moore-Penrose, core and dual core inverse in rings with involution

DOI10.1016/j.laa.2014.09.003zbMath1297.15006arXiv1403.8108OpenAlexW2019498037MaRDI QIDQ744119

Nebojša Č. Dinčić, Dragan S. Rakić, Dragan S. Djordjević

Publication date: 6 October 2014

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

Full work available at URL: https://arxiv.org/abs/1403.8108

zbMATH Keywords

idempotentMoore-Penrose inversegroup inversecore inversering with involutionEP element\((b,c)\)-inversecore-EP generalized inversedual core inverseinverse along an element

Mathematics Subject Classification ID

Theory of matrix inversion and generalized inverses (15A09) Matrices over special rings (quaternions, finite fields, etc.) (15B33) Rings with involution; Lie, Jordan and other nonassociative structures (16W10)

Related Items (only showing first 100 items - show all)

*-DMP elements in *-semigroups and *-rings ⋮ CHARACTERIZATIONS OF ANNIHILATOR (b, c)-INVERSES IN ARBITRARY RINGS ⋮ Perturbation bounds for the core inverse of matrices ⋮ A new class of generalized inverses in semigroups and rings with involution ⋮ The structures and properties of some generalized invertible operators ⋮ Weak group inverses and partial isometries in proper *-rings ⋮ Weak core inverses and pseudo core inverses in a ring with involution ⋮ The \(\{ 1 , 2 , 3 , 1^m \}\)-inverses: a generalization of core inverses for matrices ⋮ Star, sharp, core and dual core partial order in rings with involution ⋮ Unnamed Item ⋮ Displacement structure of the core inverse ⋮ Projections for generalized inverses ⋮ Further results of special elements in rings with involution ⋮ On a weighted core inverse in a ring with involution ⋮ The pseudo core inverses of differences and products of projections in rings with involution ⋮ Characterizations and maximal classes of elements related to pseudo core inverses ⋮ Three limit representations of the core-EP inverse ⋮ Additive perturbations and multiplicative perturbations for the core inverse of bounded linear operator in Hilbert space ⋮ Core inverse in Banach algebras ⋮ The one-sided inverse along an element in semigroups and rings ⋮ On elements whose Moore–Penrose inverse is idempotent in a*-ring ⋮ Characterizations of weighted core inverses in rings with involution ⋮ The (b,c)-inverse for products and lower triangular matrices ⋮ Characterizations of the weighted core-EP inverses ⋮ New characterizations for core inverses in rings with involution ⋮ Unnamed Item ⋮ On forward-order law for core inverse in rings ⋮ Further results on weighted core-EP inverse of matrices ⋮ \(m\)-weak group inverses in a ring with involution ⋮ The core inverse of a product and \(2\times 2\) matrices ⋮ On characterizations of special elements in rings with involution ⋮ Characterizations and representations of the inverse along an element ⋮ Weak group inverses in proper ∗-rings ⋮ The core and dual core inverse of a morphism with factorization ⋮ Revisitation of the core inverse ⋮ Characterizations for pseudo core inverses in a ring with involution ⋮ Weighted pseudo core inverses in rings ⋮ Characterizations of *-DMP matrices over rings ⋮ Characterizations of core and dual core inverses in rings with involution ⋮ Several characterizations for generalized inverses in a ring ⋮ Pseudo core inverses in rings with involution ⋮ Composite outer inverses for rectangular matrices ⋮ Further results on several types of generalized inverses ⋮ Absorption laws and reverse order laws for generalized core inverses ⋮ Existence criteria and expressions of the \((b,c)\)-inverse in rings and their applications ⋮ Characterizations of m-EP elements in rings ⋮ Representations of the (b,c)-inverses in rings with involution ⋮ On *-DMP inverses in a ring with involution ⋮ Generalized WG inverse ⋮ The $(j,m)$-core inverse in rings with involution ⋮ Weighted quaternion core-EP, DMP, MPD, and CMP inverses and their determinantal representations ⋮ Partial orders in rings based on generalized inverses -- unified theory. ⋮ Determinantal representations of the quaternion core inverse and its generalizations ⋮ EP elements in rings with involution ⋮ Reverse order law for the core inverse in rings ⋮ The forward order laws for the core inverse ⋮ The \((b, c)\)-inverse in semigroups and rings with involution ⋮ New results on (b, c)–inverses ⋮ Right core inverses of a product and a companion matrix ⋮ The group inverse and core inverse of sums of two elements in a ring ⋮ One-sided core partial orders on a ring with involution ⋮ The Existence of Generalized Inverses of Fuzzy Matrices ⋮ Weighted Moore-Penrose inverses and weighted core inverses in rings with involution ⋮ Characterizations and representations of the core inverse and its applications ⋮ Characterizations and representations of outer inverse for matrices over a ring ⋮ On most perfect magic squares of order four ⋮ Determinantal representations of the core inverse and its generalizations with applications ⋮ From projectors to 1MP and MP1 generalized inverses and their induced partial orders ⋮ Core and core-EP inverses of tensors ⋮ The core invertibility of a companion matrix and a Hankel matrix ⋮ On the continuity and differentiability of the (dual) core inverse in C*-algebras ⋮ Weighted (b,c)-inverses in categories and semigroups ⋮ Core invertibility of triangular matrices over a ring ⋮ Group inverse and core inverse in Banach and C*-algebras ⋮ The characterizations of one-sided generalized inverses ⋮ The pseudo core inverse of a lower triangular matrix ⋮ Right core inverse and the related generalized inverses ⋮ Centralizer's applications to the \((b, c)\)-inverses in rings ⋮ Left core inverses in rings with involution ⋮ Projections generated by Moore–Penrose inverses and core inverses ⋮ The core and dual core inverse of a morphism with kernel ⋮ On the intrinsic structure of the solution set to the Yang-Baxter-like matrix equation ⋮ Determinantal representations of the weighted core-EP, DMP, MPD, and CMP inverses ⋮ On 2MP-, MP2- and C2MP-inverses for rectangular matrices ⋮ Several types of one-sided partial orders in rings ⋮ The core inverses of differences and products of projections in rings with involution ⋮ Integral representations of two generalized core inverses ⋮ Optimal perturbation bounds for the core inverse ⋮ Properties of core-EP order in rings with involution ⋮ Rank equalities related to the generalized inverses \(A^{\Vert (B_1,C_1)}\), \(D^{\Vert(B_2,C_2)}\) of two matrices \(A\) and \(D\) ⋮ The core inverses of linear combinations of two core invertible matrices ⋮ Core–EP inverses in Banach algebras ⋮ Core and dual core inverses of a sum of morphisms ⋮ Rank equalities related to a class of outer generalized inverse ⋮ The Moore-Penrose inverse in rings with involution ⋮ Core partial order in rings with involution ⋮ Pseudo core inverses of a sum of morphisms ⋮ Additive properties for the pseudo core inverse of morphisms in an additive category ⋮ On some orders in ∗-rings based on the core-EP decomposition ⋮ The CEPGD-inverse for square matrices

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On generalized inverses and Green's relations
• Moore-Penrose inverse in rings with involution
• EP elements in rings.
• Generalized inverses. Theory and applications.
• A class of outer generalized inverses
• Core inverse of matrices
• On generalized inverses in C*-algebras
• Core–EP inverse

This page was built for publication: Group, Moore-Penrose, core and dual core inverse in rings with involution