کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
9498182 | 1631192 | 2005 | 15 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Rational realizations of the minimum rank of a sign pattern matrix
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
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چکیده انگلیسی
A sign pattern matrix is a matrix whose entries are from the set {+, â, 0}. The minimum rank of a sign pattern matrix A is the minimum of the ranks of the real matrices whose entries have signs equal to the corresponding entries of A. It is conjectured that the minimum rank of every sign pattern matrix can be realized by a rational matrix. The equivalence of this conjecture to several seemingly unrelated statements are established. For some special cases, such as when A is entrywise nonzero, or the minimum rank of A is at most 2, or the minimum rank of A is at least n â 1 (where A is m Ã n), the conjecture is shown to hold. Connections between this conjecture and the existence of positive rational solutions of certain systems of homogeneous quadratic polynomial equations with each coefficient equal to either â1 or 1 are investigated.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Linear Algebra and its Applications - Volume 409, 1 November 2005, Pages 111-125
Journal: Linear Algebra and its Applications - Volume 409, 1 November 2005, Pages 111-125
نویسندگان
Marina Arav, Frank J. Hall, Selcuk Koyuncu, Zhongshan Li, Bhaskara Rao,