报告人：李忠善 教授 （美国Georgia 州立大学）
时间：2012年6月19日（周二）下午1点
地点：闵行数学楼102报告厅
题目：Sign patterns with minimum rank 2 and upper bounds on minimum ranks
摘要： A sign pattern (matrix) is a matrix whose entries are from the set {+, -, 0}. The minimum rank (resp., rational minimum rank) of a sign pattern matrix A is the minimum of the ranks of the real (resp., rational) matrices whose entries have signs equal to the corresponding entries of A. The notion of a condensed sign pattern is introduced.
A new, insightful proof of the rational realizability of the minimum rank of a sign pattern with minimum rank 2 is obtained. Several characterizations of sign patterns with minimum rank 2 are established, long with linear upper bounds for the absolute values of an integer matrix achieving the minimum rank 2. A known upper bound for the minimum rank of a (+,-) sign pattern
