Partial orderings of matrices referring to singular values or eigenvalues

DOI10.1016/0024-3795(87)90333-8zbMath0627.15005OpenAlexW2026200717WikidataQ127030975 ScholiaQ127030975MaRDI QIDQ581501

Jerzy K. Baksalary, Jan Hauke

Publication date: 1987

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

Full work available at URL: https://doi.org/10.1016/0024-3795(87)90333-8

zbMATH Keywords

Hermitian matricessingular valuescomplex matricespartial isometriespartial orderingminus orderingstar orderingCochran's theorem

Mathematics Subject Classification ID

Eigenvalues, singular values, and eigenvectors (15A18) Algebraic systems of matrices (15A30) Quadratic and bilinear forms, inner products (15A63) Ordered rings, algebras, modules (06F25)

Related Items (9)

A further algebraic version of Cochran's theorem and matrix partial orderings ⋮ Monotone Linear Transformations on Matrices Are Invertible ⋮ Monotone additive matrix transformations ⋮ Remarks on the sharp partial order and the ordering of squares of matrices ⋮ Combinatorial methods in algebra. Transl. from the Russian ⋮ Left-star and right-star partial orderings ⋮ Some properties of matrix partial orderings ⋮ A note on the rank-subtractivity ordering ⋮ Partial orderings, preorderings, and the polar decomposition of matrices

Cites Work

• On some characterizations of the star partial ordering for matrices and rank subtractivity
• Some closed form formulae for the intersection of two special matrices under the star order
• A note on rank-additivity
• 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
• The Distribution of a Quadratic Form of Normal Random Variables
• Inequalities: theory of majorization and its applications
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