Polyhedral cones and positive operators
نویسندگان
چکیده
منابع مشابه
Lyapunov rank of polyhedral positive operators
IfK is a closed convex cone and if L is a linear operator having L (K) ⊆ K, then L is a positive operator on K and L preserves inequality with respect to K. The set of all positive operators on K is denoted by π (K). If K∗ is the dual of K, then its complementarity set is C (K) := {(x, s) ∈ K ×K | 〈x, s〉 = 0} . Such a set arises as optimality conditions in convex optimization, and a linear oper...
متن کاملBruhat Intervals and Polyhedral Cones
Lecture notes by Matthew Dyer for lectures at the workshop “Coxeter groups and convex geometry.” 1. Root labelled Bruhat graph 1.1. Bruhat order. Let (W,S) be a Coxeter group. Bruhat order is the partial order defined by the following proposition; see [3] and [13] for more details. Proposition. There is a partial order ≤ on W with the following properties. Let w ∈ W and w = s1 . . . sn, n = l0(...
متن کاملPositive and Z-operators on closed convex cones
Let K be a closed convex cone with dual K∗ in a finite-dimensional real Hilbert space V . A positive operator on K is a linear operator L on V such that L (K) ⊆ K. Positive operators generalize the nonnegative matrices and are essential to the Perron-Frobenius theory. We say that L is a Z-operator on K if 〈L (x), s〉 ≤ 0 for all (x, s) ∈ K ×K such that 〈x, s〉 = 0. The Z-operators are generalizat...
متن کاملSome results of polyhedral cones and simplicial cones
This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden. The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date...
متن کاملPolyhedral Combinatorics of UPGMA Cones
Distance-based methods such as UPGMA (Unweighted Pair Group Method with Arithmetic Mean) continue to play a significant role in phylogenetic research. We use polyhedral combinatorics to analyze the natural subdivision of the positive orthant induced by classifying the input vectors according to tree topologies returned by the algorithm. The partition lattice informs the study of UPGMA trees. We...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1974
ISSN: 0024-3795
DOI: 10.1016/0024-3795(74)90089-5