کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4602745 1336936 2008 11 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Unitary matrix digraphs and minimum semidefinite rank
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
Unitary matrix digraphs and minimum semidefinite rank
چکیده انگلیسی

For an undirected simple graph G, the minimum rank among all positive semidefinite matrices with graph G is called the minimum semidefinite rank (msr) of G. In this paper, we show that the msr of a given graph may be determined from the msr of a related bipartite graph. Finding the msr of a given bipartite graph is then shown to be equivalent to determining which digraphs encode the zero/nonzero pattern of a unitary matrix. We provide an algorithm to construct unitary matrices with a certain pattern, and use previous results to give a lower bound for the msr of certain bipartite graphs.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Linear Algebra and its Applications - Volume 428, Issue 7, 1 April 2008, Pages 1685-1695