Monotone Linear Transformations on Matrices Are Invertible

DOI10.1081/AGB-200058398zbMath1082.15002MaRDI QIDQ5704518

Anna A. Alieva, Alexander E. Guterman

Publication date: 15 November 2005

Published in: Communications in Algebra (Search for Journal in Brave)

zbMATH Keywords

linear preserversmonotone transformationmatrix partial orders

Mathematics Subject Classification ID

Positive matrices and their generalizations; cones of matrices (15B48) Linear transformations, semilinear transformations (15A04) Ordered rings, algebras, modules (06F25)

Related Items (7)

Additive matrix maps that are monotone with respect to the orders induced by the group inverse ⋮ Monotone maps on matrices of index one ⋮ Weighted G-Drazin inverses and a new pre-order on rectangular matrices ⋮ On some new pre-orders defined by weighted Drazin inverses ⋮ Maps preserving the diamond partial order ⋮ Monotone additive matrix transformations ⋮ Combinatorial methods in algebra. Transl. from the Russian

Cites Work

• Unnamed Item
• 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
• Linear transformations on matrices: The invariance of sets of ranks
• Linear preserver problems: A brief introduction and some special techniques
• A note on the rank-subtractivity ordering
• Linear operators that preserve pairs of matrices which satisfy extreme rank properties -- a supplementary version.
• Linear operators that preserve pairs of matrices which satisfy extreme rank properties
• Some properties of matrix partial orderings
• Linear transformations which preserve Hermitian and positive semidefinite operators
• Transformations on tensor spaces
• Linear transformations of tensor products preserving a fixed rank
• Sur une généralisation du groupe orthogonal à quatre variables
• LINEAR PRESERVERS FOR DRAZIN STAR PARTIAL ORDER
• Linear transformations on tensor spaces
• The natural partial order on a regular semigroup
• Natural structures on semigroups with involution
• Linear preservers for matrix inequalities and partial orderings

This page was built for publication: Monotone Linear Transformations on Matrices Are Invertible