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Seminar第1550期 Sign patterns that allow diagonalizability

创建日期 2017/12/4 福平   浏览次数  59 返回    
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报告主题:Sign patterns that allow diagonalizability
报告人:Prof. Zhongshan Li (Georgia State University)
报告时间:2017年 12月11日(周一)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 $\{+,-, 0 \}$. A square sign pattern $\cal A$ is said to allow diagonalizability if there is a diagonalizable real matrix whose entries have signs specified by the corresponding entries of $\cal A$. Characterization of sign patterns that allow diagonalizability has been a long-standing open problem.
It is known that a sign pattern allows diagonalizability if and only if it allows rank principality. In this talk, we establish some new necessary/sufficient conditions for a sign pattern to allow diagonalizability, and explore possible ranks of diagonalizable matrices with a specified sign pattern. In particular, it is shown that every irreducible sign pattern with minimum rank 2 allows diagonalizability at rank 2 and also at the maximum rank.

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