Maximal elements under the three partial orders

DOI10.1016/0024-3795(92)90301-PzbMath0767.15017MaRDI QIDQ1200551

Robert E. Hartwig, Raphael Loewy

Publication date: 16 January 1993

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

zbMATH Keywords

projectionsidempotentsnilpotent matricespartial ordersunitary matricesmaximal elementscontractionsstar orderminus orderpositive semidefinite order

Mathematics Subject Classification ID

Norms of matrices, numerical range, applications of functional analysis to matrix theory (15A60) Miscellaneous inequalities involving matrices (15A45) Convex sets and cones of operators (47L07) Ordered rings, algebras, modules (06F25) Ordered topological linear spaces, vector lattices (46A40)

Related Items (3)

Partial orders based on inverses along elements ⋮ Order intervals of matrices ⋮ On generalized quadratic matrices

Cites Work

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• On some characterizations of the star partial ordering for matrices and rank subtractivity
• Existence and comparison theorems for algebraic Riccati equations for continuous- and discrete-time systems
• Lattice properties of the *-order for complex matrices
• Natural structures on semigroups with involution
• Conditions for Positive and Nonnegative Definiteness in Terms of Pseudoinverses

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