On the Löwner, minus, and star partial orderings of nonnegative definite matrices and their squares

DOI10.1016/0024-3795(91)90359-5zbMath0737.15008OpenAlexW1972689707MaRDI QIDQ1174776

Jerzy K. Baksalary, Friedrich Pukelsheim

Publication date: 25 June 1992

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

Full work available at URL: https://doi.org/10.1016/0024-3795(91)90359-5

zbMATH Keywords

partial orderingscommutativityminus orderingstar orderingLöwner orderingHermitian nonnegative definite matrices

Mathematics Subject Classification ID

Commutativity of matrices (15A27) Positive matrices and their generalizations; cones of matrices (15B48) Miscellaneous inequalities involving matrices (15A45)

Related Items (20)

Preorderings, monotone functions, and best rank \(r\) approximations with applications to classical MDS ⋮ Properties of the star supremum for arbitrary Hilbert space operators ⋮ Characterizations of minus and star orders between the squares of Hermitian matrices ⋮ Space pre-order and minus partial order for operators on Banach spaces ⋮ Some remarks on partial orderings of nonnegative definite matrices ⋮ On semi-star-related matrices ⋮ A new partial order based on core partial order and star partial order ⋮ A game approach to multi-dimensional opinion dynamics in social networks with stubborn strategist agents ⋮ Further relationships between certain partial orders of matrices and their squares. ⋮ Solving a minus partial ordering equation over von Neumann regular rings. ⋮ Relationships between partial orders of matrices and their powers. ⋮ Some further results on Hermitian-matrix inequalities ⋮ Unnamed Item ⋮ Löwner partial ordering and space preordering of Hermitian non-negative definite matrices ⋮ Solutions of minus partial ordering equations over von Neumann regular rings ⋮ Inter- and extrapolatory properties of matrix partial orderings ⋮ On bounding the Thompson metric by Schatten norms ⋮ A note on the star order in Hilbert spaces ⋮ Constrained matrix optimization with applications ⋮ The polar-like decomposition and its applications

Cites Work

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• Two orderings on a convex cone of nonnegative definite matrices
• The matrix inequality \(M \leq B^*MB\)
• On some characterizations of the star partial ordering for matrices and rank subtractivity
• The rank of a difference of matrices and associated generalized inverses
• Natural structures on semigroups with involution
• Some Inequalities for Positive Definite Symmetric Matrices
• Inequalities: theory of majorization and its applications

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