报告题目：Sign patterns that allow diagonalization

报告专家：Professor Zhongshan Li, Georgia State University

报告时间：2018年6月29 日(周五)  15：00

报告地点：7JC段306

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 diagonalization 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 diagonalization has been a long-standing open problem. It is known that a sign pattern allows diagonalization if and only if it allows rank-principality. In this talk, we establish some new necessary/sufficient conditions for a sign pattern to allow diagonalization, 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 diagonalization at rank 2 and also at the maximum rank. Sign patterns whose maximal zero submatrices are strongly disjoint are shown to allow diagonalization with the maximum rank.

主讲人简介：

    李忠善（Zhongshan Li）, 教授，男，现为美国Georgia State University（佐治亚州立大学）数学系终身正教授。2010年至2015年担任佐治亚州立大学数学系研究生部主任，并于2010年成为佐治亚州立大学科学与艺术学院职称和终身教授评定委员会的成员, 2017年起任此委员会的主席。

李忠善教授目前主要从事组合矩阵论的研究，包括符号模式矩阵、最小秩问题、非负矩阵、代数图论、整数矩阵、矩阵方程的有理解、实线性子空间的符号向量集等。李教授在《American Mathematical Monthly》，《Linear Algebra and Its Applications》， 《SIAM J. on Discrete Math.》，《Linear and Multilinear Algebra》， 《J. Combin. Theory Ser. B》， 《IEEE Transactions on Neural Networks and Learning Systems》 等重要国际学术期刊上发表论文60余篇，并出版学术专著《Handbook of Linear Algebra》，主持或参与多项科研项目。目前,李教授还担任美国《Mathematical Reviews》特约评论员，《JP Journal of Algebra，Number Theory and Applications》杂志编委，美国数学会会员，国际线性代数学会会员等职务。

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