Further properties of the star, left-star, right-star, and minus partial orderings.

DOI10.1016/S0024-3795(03)00609-8zbMath1048.15016MaRDI QIDQ1414696

Xiaoji Liu, Oskar Maria Baksalary, Jerzy K. Baksalary

Publication date: 4 December 2003

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

zbMATH Keywords

Hermitian matrixmatrix partial orderingspartial isometrynormal matrixorthogonal projectorEP matrix

Mathematics Subject Classification ID

Positive matrices and their generalizations; cones of matrices (15B48) Hermitian, skew-Hermitian, and related matrices (15B57)

Related Items (19)

Properties of the star supremum for arbitrary Hilbert space operators ⋮ Further properties of generalized and hypergeneralized projectors ⋮ Some new results on the core partial order ⋮ Further properties on the core partial order and other matrix partial orders ⋮ The supremum of linear operators for the *-order ⋮ Star, left-star, and right-star partial orders in Rickart ∗-rings ⋮ 1MP and MP1 inverses and one-sided star orders in a ring with involution ⋮ Certain properties of T-EP operators ⋮ Further relationships between certain partial orders of matrices and their squares. ⋮ Some properties on the star order of bounded operators ⋮ Further results on generalized and hypergeneralized projectors ⋮ The diamond partial order in rings ⋮ Remarks on the sharp partial order and the ordering of squares of matrices ⋮ Some results on partial ordering and reverse order law of elements of \(C^{*}\)-algebras ⋮ Left-star order structure of Rickart *-rings ⋮ On the properties of weakly parallel summable operators ⋮ Automorphisms of Mn, partially ordered by the star order ⋮ Some results on characterizations of matrix partial orderings ⋮ Some relations of projection and star order in Hilbert space

Cites Work

• Unnamed Item
• Left-star and right-star partial orderings
• Inheriting independence and chi-squaredness under certain matrix orderings
• On some characterizations of the star partial ordering for matrices and rank subtractivity
• Partial orderings, preorderings, and the polar decomposition of matrices
• A property of orthogonal projectors
• Projections, generalized inverses, and quadratic forms
• Some closed form formulae for the intersection of two special matrices under the star order
• The natural partial order on a regular semigroup
• Natural structures on semigroups with involution

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