Linear equations over cones with interior: a solvability theorem with applications to matrix theory

Abraham Berman; Adi Ben-Israel

doi:10.1016/0024-3795(73)90048-7

Linear equations over cones with interior: a solvability theorem with applications to matrix theory

Abraham Berman, Adi Ben-Israel

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

Abstract

The solvability of linear equations with solutions in the interior of a closed convex cone is characterized. Corollaries include Lyapunov's theorem characterizing stable matrices and a generalization of Stiemke's theorem of the alternative for complex linear inequalities.

Original language	English (US)
Pages (from-to)	139-149
Number of pages	11
Journal	Linear Algebra and Its Applications
Volume	7
Issue number	2
DOIs	https://doi.org/10.1016/0024-3795(73)90048-7
State	Published - Apr 1973
Externally published	Yes

All Science Journal Classification (ASJC) codes

Algebra and Number Theory
Numerical Analysis
Geometry and Topology
Discrete Mathematics and Combinatorics

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10.1016/0024-3795(73)90048-7

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title = "Linear equations over cones with interior: a solvability theorem with applications to matrix theory",

abstract = "The solvability of linear equations with solutions in the interior of a closed convex cone is characterized. Corollaries include Lyapunov's theorem characterizing stable matrices and a generalization of Stiemke's theorem of the alternative for complex linear inequalities.",

author = "Abraham Berman and Adi Ben-Israel",

year = "1973",

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Linear equations over cones with interior: a solvability theorem with applications to matrix theory

Abstract

All Science Journal Classification (ASJC) codes

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