Characterizations of the core inverse and the core partial ordering

DOI10.1080/03081087.2014.975702zbMath1325.15002OpenAlexW2095326720MaRDI QIDQ2943850

Publication date: 4 September 2015

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

Full work available at URL: https://doi.org/10.1080/03081087.2014.975702

zbMATH Keywords

generalized inverse singular values Moore-Penrose inverse core inverse reverse-order law core partial ordering

Mathematics Subject Classification ID

Partial orders, general (06A06) Factorization of matrices (15A23) Theory of matrix inversion and generalized inverses (15A09) Eigenvalues, singular values, and eigenvectors (15A18)

Related Items (49)

Regular factorizations and perturbation analysis for the core inverse of linear operators in Hilbert spaces ⋮ Perturbation bounds for the core inverse of matrices ⋮ The structures and properties of some generalized invertible operators ⋮ GDMP-inverses of a matrix and their duals ⋮ Some new results on the core partial order ⋮ Core-EP decomposition and its applications ⋮ The \(\{ 1 , 2 , 3 , 1^m \}\)-inverses: a generalization of core inverses for matrices ⋮ Displacement structure of the core inverse ⋮ Three limit representations of the core-EP inverse ⋮ Characterizations, iterative method, sign pattern and perturbation analysis for the DMP inverse with its applications ⋮ Reverse order laws on the conditions of the commutativity up to a factor ⋮ Methods of Gauss–Jordan elimination to compute core inverse and dual core inverse ⋮ The Core-EP, Weighted Core-EP Inverse of Matrices and Constrained Systems of Linear Equations ⋮ Further results on strongly core orthogonal matrix ⋮ The class ofm-EPandm-normal matrices ⋮ Partial orders based on core-nilpotent decomposition ⋮ Characterizations of the weighted core-EP inverses ⋮ New characterizations for core inverses in rings with involution ⋮ Lattice properties of partial orders for complex matrices via orthogonal projectors ⋮ A new partial order based on core partial order and star partial order ⋮ Matrix derivatives and Kronecker products for the core and generalized core inverses ⋮ Further results on weighted core-EP inverse of matrices ⋮ The core inverse of a product and \(2\times 2\) matrices ⋮ The core and dual core inverse of a morphism with factorization ⋮ Revisitation of the core inverse ⋮ Some theorems on the core inverse of matrices and the core partial ordering ⋮ A partial order on the set of complex matrices with index one ⋮ Solutions of the matrix inequality \(AXA\overset{?}{\leq}A\) in some partial orders ⋮ Sign pattern, usability, representations and perturbation for the core-EP and weighted core-EP inverse ⋮ Remark on the core-EP pre-order of Hilbert space operators ⋮ The weak group matrix ⋮ Compute lim_{λ → 0}X(λI_p+YAX)⁻¹Yby the product singular value decomposition ⋮ Reverse order law for the core inverse in rings ⋮ Characterizations of k-commutative equalities for some outer generalized inverses ⋮ The 𝔪-core inverse and its applications ⋮ The group inverse and core inverse of sums of two elements in a ring ⋮ Characterizations and representations of the core inverse and its 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 ⋮ The core inverse and constrained matrix approximation problem ⋮ Core invertibility of triangular matrices over a ring ⋮ On 2MP-, MP2- and C2MP-inverses for rectangular matrices ⋮ Integral representations of two generalized core inverses ⋮ Optimal perturbation bounds for the core inverse ⋮ The core inverses of linear combinations of two core invertible matrices ⋮ Core partial order in rings with involution ⋮ Weighted weak core inverse of operators ⋮ Characterizations and representations for the CMP inverse and its application

Cites Work

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