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 R^m′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(xué)）數(shù)學(xué)系終身正教授。研究方向包括組合矩陣?yán)碚摗⒋鷶?shù)圖論、矩陣?yán)碚搼?yīng)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(xué)術(shù)期刊上發(fā)表論文80余篇，并撰寫了學(xué)術(shù)專著《Handbook of Linear Algebra》中關(guān)于符號模式矩陣的一章，主持或參與多項科研項目。目前擔(dān)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(wù)。08-09年，15-16年， 和18-19年擔(dān)任加拿大國家科學(xué)和工程研究委員會項目評審專家。