摘要：Given an m´n real matrix A, the set of all real matrices with the same size and the same rank as A forms a smooth manifold. The set of all real matrices whose entries have the same sign as the corresponding entry of the matrix A forms another smooth manifold. When the tangent spaces of these two manifolds at A sum to Rm´n , we say that A has the rank-preserving transversality property (RPTP). In this talk, we explore the RPTP. In particular, we present some fundamental results on the RPTP, the sign patterns and zero-nonzero patterns that require or allow the RPTP, and some open problems.
报告人简介：李忠善(Zhongshan Li)教授，美国Georgia State University（佐治亚州立大学）数学系终身正教授。研究方向包括组合矩阵理论、代数图论、矩阵理论应用等。曾在《American Mathematical Monthly》，《Linear Algebra and Its Applications》，《SIAM J. on Discrete Mathematics》，《J. Combin. Theory Ser. B》，《Linear and Multilinear Algebra》， 《Graphs and Combinatorics》，《IEEE Transactions on Neural Networks and Learning Systems》 等重要国际学术期刊上发表论文80余篇，并撰写了学术专著《Handbook of Linear Algebra》中关于符号模式矩阵的一章，主持或参与多项科研项目。目前担任美国《Mathematical Reviews》特约评论员，《JP Journal of Algebra，Number Theory and Applications》和《Special Matrices》杂志编委等职务。08-09年，15-16年， 和18-19年担任加拿大国家科学和工程研究委员会项目评审专家。
