報告題目:Sign patterns that allow diagonalization
報告專家:Professor Zhongshan Li,Georgia State University
報告時間:2018年6月29日(周五) 15:00
報告地點: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.
主講人簡介:
李忠善(Zhongshan Li),教授三亚娱乐官方网站,男三亚娱乐官方网站,現為美國Georgia State University(佐治亞州立大學)數學系終身正教授三亚娱乐官方网站。2010年至2015年擔任佐治亞州立大學數學系研究生部主任三亚娱乐官方网站,并于2010年成為佐治亞州立大學科學與藝術學院職稱和終身教授評定委員會的成員, 2017年起任此委員會的主席。
李忠善教授目前主要從事組合矩陣論的研究三亚娱乐官方网站,包括符號模式矩陣、最小秩問題三亚娱乐官方网站、非負矩陣、代數圖論、整數矩陣三亚娱乐官方网站、矩陣方程的有理解、實線性子空間的符號向量集等。李教授在《American Mathematical Monthly》,《Linear Algebra and Its Applications》,《SIAM J. on Discrete Math.》,《Linear and Multilinear Algebra》三亚娱乐官方网站,《J. Combin. Theory Ser. B》三亚娱乐官方网站,《IEEE Transactions on Neural Networks and Learning Systems》等重要國際學術期刊上發表論文60余篇三亚娱乐官方网站,并出版學術專著《Handbook of Linear Algebra》,主持或參與多項科研項目。目前,李教授還擔任美國《Mathematical Reviews》特約評論員,《JP Journal of Algebra,Number Theory and Applications》雜志編委,美國數學會會員三亚娱乐官方网站,國際線性代數學會會員等職務。
歡迎各位老師參加!