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.
報告人簡介：李忠善(Zhongshan Li)教授，美國Georgia State University（佐治亞州立大學）數(shù)學系終身正教授。研究方向包括組合矩陣理論、代數(shù)圖論、矩陣理論應用等。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》 等重要國際學術期刊上發(fā)表論文80余篇，并撰寫了學術專著《Handbook of Linear Algebra》中關于符號模式矩陣的一章，主持或參與多項科研項目。目前擔任美國《Mathematical Reviews》特約評論員，《JP Journal of Algebra，Number Theory and Applications》和《Special Matrices》雜志編委等職務。08-09年，15-16年， 和18-19年擔任加拿大國家科學和工程研究委員會項目評審專家。
