Further properties on the core partial order and other matrix partial orders

DOI10.1080/03081087.2013.839676zbMath1306.15030OpenAlexW1984582337MaRDI QIDQ2929497

Saroj B. Malik, Laura Rueda, Nestor Janier Thome

Publication date: 12 November 2014

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

Full work available at URL: http://hdl.handle.net/10251/57052

zbMATH Keywords

matrix decompositionstar partial ordercore inversecore partial orderminus partial orderdiamond partial orderHartwig-Spindelböck decomposition

Mathematics Subject Classification ID

Theory of matrix inversion and generalized inverses (15A09) Positive matrices and their generalizations; cones of matrices (15B48) Miscellaneous inequalities involving matrices (15A45)

Related Items (28)

Some new results on the core partial order ⋮ On star, sharp, core, and minus partial orders in Rickart rings ⋮ Star, sharp, core and dual core partial order in rings with involution ⋮ Further results on partial ordering and the generalized inverses ⋮ The Core-EP, Weighted Core-EP Inverse of Matrices and Constrained Systems of Linear Equations ⋮ Partial orders based on core-nilpotent decomposition ⋮ Further results on weighted core inverse in a ring ⋮ A simultaneous canonical form of a pair of matrices and applications involving the weighted Moore-Penrose inverse ⋮ Lattice properties of partial orders for complex matrices via orthogonal projectors ⋮ Core–EP pre-order of Hilbert space operators ⋮ Revisitation of the core inverse ⋮ Relationships between DMP relation and some partial orders ⋮ Revisiting the core EP inverse and its extension to rectangular matrices ⋮ Weak group inverse ⋮ Weighted pre-orders involving the generalized Drazin inverse ⋮ Some theorems on the core inverse of matrices and the core partial ordering ⋮ Solutions of the matrix inequality \(AXA\overset{?}{\leq}A\) in some partial orders ⋮ A partial ordering approach to characterize properties of a pair of orthogonal projectors ⋮ Partial orders in rings based on generalized inverses -- unified theory. ⋮ New matrix partial order based on spectrally orthogonal matrix decomposition ⋮ Sharp partial order and linear autonomous systems ⋮ Left and right generalized Drazin invertible operators on Banach spaces and applications ⋮ Ordered matrices with nonnegative group projector ⋮ On some partial orders on a certain subset of the power set of rings ⋮ Generalization of sharp and core partial order using annihilators ⋮ The new revisitation of core EP inverse of matrices ⋮ Core partial order in rings with involution ⋮ Partial orders on \(\mathcal{B}(\mathcal{H})\)

Cites Work

• Invertibility of a linear combination of two matrices and partial orderings
• A further algebraic version of Cochran's theorem and matrix partial orderings
• On a matrix decomposition of Hartwig and Spindelböck
• On the Drazin index of regular elements
• Partial orderings, preorderings, and the polar decomposition of matrices
• Further properties of the star, left-star, right-star, and minus partial orderings.
• Generalized inverses. Theory and applications.
• Reverse order law for the group inverse in rings
• Space pre-order and minus partial order for operators on Banach spaces
• Matrices for whichA^∗andA^†commute
• Core inverse of matrices
• Note on the core matrix partial ordering

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