Universally optimal matrices and field independence of the minimum rank of a graph
نویسندگان
چکیده
منابع مشابه
Ela Universally Optimal Matrices and Field Independence of the Minimum Rank of a Graph∗
The minimum rank of a simple graph G over a field F is the smallest possible rank among all symmetric matrices over F whose (i, j)th entry (for i = j) is nonzero whenever {i, j} is an edge in G and is zero otherwise. A universally optimal matrix is defined to be an integer matrix A such that every off-diagonal entry of A is 0, 1, or −1, and for all fields F , the rank of A is the minimum rank o...
متن کاملUniversally Optimal Matrices and Field Independence of the Minimum Rank of a Graph∗
The minimum rank of a simple graph G over a field F is the smallest possible rank among all symmetric matrices over F whose ijth entry (for i != j) is nonzero whenever {i, j} is an edge in G and is zero otherwise. We define a universally optimal matrix to be an integer matrix A such that every off-diagonal entry of A is 0, 1, or −1, and for all fields F , the rank of A is the minimum rank over ...
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ژورنال
عنوان ژورنال: The Electronic Journal of Linear Algebra
سال: 2009
ISSN: 1081-3810
DOI: 10.13001/1081-3810.1321