Valeurs propres relatives à un cône convexe : caractérisation et résultats de cardinalité
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Let A be an n×n real matrix, and K
Rn be a closed convex cone. The spectrum of A relative to K, denoted by σ(A,K), is the set of all λ
R for which the linear complementarity problem Formula Not Shown admits a nonzero solution xRn. The aim of this Note is to study the main properties of the set-valued mapping σ(·,K), and discuss some structural differences existing between the polyhedral case (i.e., K is finitely generated) and the non-polyhedral case. To cite this article: A. Seeger, M. Torki, C. R. Acad. Sci. Paris, Ser. I 336 (2003).
Rn be a closed convex cone. The spectrum of A relative to K, denoted by σ(A,K), is the set of all λR for which the linear complementarity problem Formula Not Shown admits a nonzero solution xRn. The aim of this Note is to study the main properties of the set-valued mapping σ(·,K), and discuss some structural differences existing between the polyhedral case (i.e., K is finitely generated) and the non-polyhedral case. To cite this article: A. Seeger, M. Torki, C. R. Acad. Sci. Paris, Ser. I 336 (2003).