A further algebraic version of Cochran's theorem and matrix partial orderings

DOI10.1016/0024-3795(90)90341-9zbMath0696.15005OpenAlexW2009303063MaRDI QIDQ910458

Jan Hauke, Jerzy K. Baksalary

Publication date: 1990

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

Full work available at URL: https://doi.org/10.1016/0024-3795(90)90341-9

zbMATH Keywords

generalized inversesminus partial orderingCochran's theoremspace preorderingstar partial orderingHermitian projections

Mathematics Subject Classification ID

Theory of matrix inversion and generalized inverses (15A09) Algebraic systems of matrices (15A30)

Related Items (28)

A note on an algebraic version of Cochran's theorem ⋮ Some new results on the core partial order ⋮ Maps preserving the truncation of products of operators ⋮ Further properties on the core partial order and other matrix partial orders ⋮ On a matrix version of Cochran's statistical theorem ⋮ Star, left-star, and right-star partial orders in Rickart ∗-rings ⋮ On some generalized inverses and partial orders in ∗-rings ⋮ On partial orders of operators ⋮ 1MP and MP1 inverses and one-sided star orders in a ring with involution ⋮ The diamond partial order for strong Rickart rings ⋮ Graphs defined by orthogonality. ⋮ Cochran's statistical theorem for outer inverses of matrices and matrix quadratic forms ⋮ Maps preserving the diamond partial order ⋮ Monotone Linear Transformations on Matrices Are Invertible ⋮ Some orders for operators on Hilbert spaces ⋮ On sets of elements in Rickart rings induced by partial orders ⋮ A partial order on the set of complex matrices with index one ⋮ A partial ordering approach to characterize properties of a pair of orthogonal projectors ⋮ The diamond partial order in rings ⋮ Monotone additive matrix transformations ⋮ Linear preservers for matrix inequalities and partial orderings ⋮ Unnamed Item ⋮ Cochran's statistical theorem revisited ⋮ Combinatorial methods in algebra. Transl. from the Russian ⋮ Automorphisms on the poset of products of two projections ⋮ Linear matrix transformations that are monotone with respect to the \(\leq^\sharp\)-or \(\leq^{\mathrm{cn}}\)-order ⋮ Partial orderings, preorderings, and the polar decomposition of matrices ⋮ On the Wedderburn-Guttman theorem

Cites Work

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• Partial orderings of matrices referring to singular values or eigenvalues
• Inheriting independence and chi-squaredness under certain matrix orderings
• On some characterizations of the star partial ordering for matrices and rank subtractivity
• A relationship between the star and minus orderings
• Relative Hermitian matrices
• The rank of a difference of matrices and associated generalized inverses
• Some properties of matrix partial orderings
• Remarks on a matrix theorem arising in statistics
• Some closed form formulae for the intersection of two special matrices under the star order
• A note on rank-additivity
• Some Matrix Results and Extensions of Cochran’s Theorem
• Errata: Some Matrix Results and Extensions of Cochran’s Theory
• Natural structures on semigroups with involution
• A note on the partial ordering of positive semi-definite matrices
• Decomposition of Symmetric Matrices and Distributions of Quadratic Forms
• Quadratic Forms and Idempotent Matrices with Random Elements

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