Theorems of the Alternative for Cones and Lyapunov Regularity of Matrices

Autor:	Daniel Hershkowitz, Bryan E. Cain, Hans Schneider
Rok vydání:	1997
Předmět:	Combinatorics Lyapunov function symbols.namesake General Mathematics Ordinary differential equation symbols Block matrix Dual polyhedron Positive-definite matrix Space (mathematics) Hermitian matrix Interior point method Mathematics
Zdroj:	Czechoslovak Mathematical Journal. 47:487-499
ISSN:	1572-9141 0011-4642
DOI:	10.1023/a:1022463518098
Popis:	Standard facts about separating linear functionals will be used to determine how two cones C and D and their duals C* and D* may overlap. When T: V → W is linear and K ⊂ V and D ⊂ W are cones, these results will be applied to C = T(K) and D, giving a unified treatment of several theorems of the alternate which explain when C contains an interior point of D. The case when V = W is the space H of n × n Hermitian matrices, D is the n × n positive semidefinite matrices, and T(X) = AX + X* A yields new and known results about the existence of block diagonal X's satisfying the Lyapunov condition: T(X) is an interior point of D. For the same V, W and D, T(X) = X − B* XB will be studied for certain cones K of entry-wise nonnegative X's.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::8e0422b7523c64e92f188a231c334e43 https://doi.org/10.1023/a:1022463518098 Zobrazit plný text záznamu Full text from SpringerLink