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Seminar第1551期 Essential sign change numbers and minimum ranks of sign patterns

创建日期 2017/12/4 福平   浏览次数  54 返回    
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报告主题:Essential sign change numbers and minimum ranks of sign patterns
报告人:Prof. Zhongshan Li (Georgia State University)
报告时间:2017年 12月12日(周二)14:00
报告地点:校本部G507
邀请人:王卿文
 
报告摘要:A sign pattern (matrix) is a matrix whose entries are from the set $\{+, -, 0\}$ and a sign vector is a vector whose entries are from the set $\{+, -, 0\}$. A sign pattern or sign vector is full if it does not contain any zero entries. The minimum rank of a sign pattern matrix $\cal A$ is the minimum of the ranks of the real matrices whose entries have signs equal to the corresponding entries of $\cal A$. The notions of essential row sign change number and essential column sign change number are introduced for full sign patterns and condensed sign patterns. By inspecting the sign vectors realized by a list of real polynomials in one variable, a lower bound on the essential row and column sign change numbers is obtained. Using point-line configurations on the plane, it is shown that even for full sign patterns with minimum rank 3, the essential row and column sign change numbers can differ greatly and can be much bigger than the minimum rank. Some open problems concerning square full sign patterns with large minimum ranks are discussed.

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