کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4602751 1336936 2008 5 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
The minimum rank problem: A counterexample
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
The minimum rank problem: A counterexample
چکیده انگلیسی

We provide a counterexample to a recent conjecture that the minimum rank over the reals of every sign pattern matrix can be realized by a rational matrix. We use one of the equivalences of the conjecture and some results from projective geometry. As a consequence of the counterexample we show that there is a graph for which the minimum rank of the graph over the reals is strictly smaller than the minimum rank of the graph over the rationals. We also make some comments on the minimum rank of sign pattern matrices over different subfields of R.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Linear Algebra and its Applications - Volume 428, Issue 7, 1 April 2008, Pages 1761-1765