On eigenvalues induced by a cone constraint
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- 作者：Seeger ; Alberto ; Torki ; Mounir
- 关键词：15A18 ; 58C40 ; Eigenvalue ; Linear complementarity problem ; Polyhedral cone ; Lorentz cone
- 刊名：Linear Algebra and its Applications
- 出版年：2003
- 出版时间：October 1, 2003
- 年：2003
- 卷：372
- 期：Complete
- 页码：181-206
- 全文大小：212 K
文摘
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 admitsa nonzero solution xRn. The notation K+ stands for the (positive) dual cone of K. The purpose of this work is to study the main properties of the mapping σ(·,K), and discuss some structural differences existing between the polyhedral case (i.e. K is finitely generated) and the nonpolyhedral case.
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 admitsa nonzero solution xRn. The notation K+ stands for the (positive) dual cone of K. The purpose of this work is to study the main properties of the mapping σ(·,K), and discuss some structural differences existing between the polyhedral case (i.e. K is finitely generated) and the nonpolyhedral case.