More on linear inequalities with applications to matrix theory

DOI10.1016/0022-247X(71)90072-2zbMath0221.15014OpenAlexW1999054827MaRDI QIDQ2547249

Abraham Berman, Adi Ben-Israel

Publication date: 1971

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-247x(71)90072-2

Mathematics Subject Classification ID

Linear inequalities of matrices (15A39) Positive matrices and their generalizations; cones of matrices (15B48) Hermitian, skew-Hermitian, and related matrices (15B57)

Related Items

Weak stability for matrices ⋮ Nonnegative definite matrices and their applications to matrix quadratic programming problems ⋮ Linear inequalities, mathematical programming and matrix theory ⋮ Linear programming with matrix variables ⋮ Applications of the Joint Angular Field of Values ⋮ On common \(\alpha\)-scalar Lyapunov solutions ⋮ Stability robustness for linear state space models -- a Lyapunov mapping approach ⋮ Feasibility and solvability of Lyapunov-type linear programming over symmetric cones ⋮ Positive diagonal solutions to the Lyapunov equations ⋮ Classes of stable and semipositive matrices ⋮ A generalization of irreducible monotonicity ⋮ Linear equations over cones with interior: a solvability theorem with applications to matrix theory ⋮ Theorems of the Alternative for Cones and Lyapunov Regularity of Matrices ⋮ Applying solvability theorems for matrix equations ⋮ A characterisation of common diagonal stability over cones

Cites Work

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• Some theorems on the inertia of general matrices
• Matrices \(C\) with \(C^ n\to 0\)
• Positive operators and an inertia theorem
• Linear equations and inequalities on finite dimensional, real or complex, vector spaces: a unified theory
• Theorems of the alternative for complex linear inequalities
• Inertia theory for simultaneously triangulable complex matrices
• Positive-definite matrices and their role in the study of the characteristic roots of general matrices
• Linear equations over cones with interior: a solvability theorem with applications to matrix theory
• A Generalization of a Theorem of Lyapunov
• Some Theorems on Commutative Matrices

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