کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4599482 1631136 2014 21 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Minimal zeros of copositive matrices
ترجمه فارسی عنوان
حداقل صفرهای ماتریس همپوشانی
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
چکیده انگلیسی

Let A   be an element of the copositive cone CnCn. A zero u of A   is a nonzero nonnegative vector such that uTAu=0uTAu=0. The support of u   is the index set suppu⊂{1,…,n} corresponding to the positive entries of u. A zero u of A is called minimal if there does not exist another zero v of A such that its support supp v is a strict subset of supp u  . We investigate the properties of minimal zeros of copositive matrices and their supports. Special attention is devoted to copositive matrices which are irreducible with respect to the cone S+(n)S+(n) of positive semi-definite matrices, i.e., matrices which cannot be written as a sum of a copositive and a nonzero positive semi-definite matrix. We give a necessary and sufficient condition for irreducibility of a matrix A   with respect to S+(n)S+(n) in terms of its minimal zeros. A similar condition is given for the irreducibility with respect to the cone NnNn of entry-wise nonnegative matrices. For n=5n=5 matrices which are irreducible with respect to both S+(5)S+(5) and N5N5 are extremal. For n=6n=6 a list of candidate combinations of supports of minimal zeros which an exceptional extremal matrix can have is provided.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Linear Algebra and its Applications - Volume 459, 15 October 2014, Pages 154–174
نویسندگان
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