Partial orderings, preorderings, and the polar decomposition of matrices

DOI10.1016/S0024-3795(98)10108-8zbMath0932.15014OpenAlexW2065968604WikidataQ127014984 ScholiaQ127014984MaRDI QIDQ1300828

Jürgen Gross, Augustyn Markiewicz, Jan Hauke

Publication date: 2 March 2000

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

Full work available at URL: https://doi.org/10.1016/s0024-3795(98)10108-8

zbMATH Keywords

Löwner partial orderingpolar decompositionpartial isometrypreorderingpartial orderingstar partial orderingrank subtractivity partial ordering

Mathematics Subject Classification ID

Factorization of matrices (15A23) Positive matrices and their generalizations; cones of matrices (15B48)

Related Items (8)

Further properties on the core partial order and other matrix partial orders ⋮ On partial orders of operators ⋮ A new partial order based on core partial order and star partial order ⋮ Further properties of the star, left-star, right-star, and minus partial orderings. ⋮ Further results on generalized and hypergeneralized projectors ⋮ A note on the rank-subtractivity ordering ⋮ Simultaneous polar decomposition of rectangular complex matrices ⋮ The polar-like decomposition and its applications

Cites Work

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• Partial orderings of matrices referring to singular values or eigenvalues
• Left-star and right-star partial orderings
• A further algebraic version of Cochran's theorem and matrix partial orderings
• Some further results on Hermitian-matrix inequalities
• Partial orders based on outer inverses
• Simultaneous polar decomposition of rectangular complex matrices
• Some properties of matrix partial orderings
• On partial orderings on the set of rectangular matrices
• Matrices for whichA^∗andA^†commute
• A note on the partial ordering of positive semi-definite matrices

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