کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
6416450 1631155 2014 33 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Characterization of tropical hemispaces by (P,R)-decompositions
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
Characterization of tropical hemispaces by (P,R)-decompositions
چکیده انگلیسی

We consider tropical hemispaces, defined as tropically convex sets whose complements are also tropically convex, and tropical semispaces, defined as maximal tropically convex sets not containing a given point. We introduce the concept of (P,R)-decomposition. This yields (to our knowledge) a new kind of representation of tropically convex sets extending the classical idea of representing convex sets by means of extreme points and rays. We characterize tropical hemispaces as tropically convex sets that admit a (P,R)-decomposition of certain kind. In this characterization, with each tropical hemispace we associate a matrix with coefficients in the completed tropical semifield, satisfying an extended rank-one condition. Our proof techniques are based on homogenization (lifting a convex set to a cone), and the relation between tropical hemispaces and semispaces.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Linear Algebra and its Applications - Volume 440, 1 January 2014, Pages 131-163
نویسندگان
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