报告题目 (Title)：Matrices with the rank-preserving transversality property (保秩横截性的矩阵)
报告人 (Speaker)： Zhongshan Li 教授（佐治亚州立大学）
报告时间 (Time)：2024年10月29 (周二) 9:00
报告地点 (Place)：腾讯会议：869-930-523
邀请人(Inviter)：谭福平
主办部门：金沙威尼斯欢乐娱人城数学系
报告摘要： Given an $m\times n$ 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 $\mathbb R^{m\times n}$, 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.
