应兰州大学数学与统计学院张和平教授和颜棋副教授邀请，佐治亚州立大学李忠善教授将于2026年7月17日至7月28日访问兰州大学并作学术报告，诚邀全校师生参加！
报告题目：Zero-nonzero patterns that allow or require the similarity-transversality property (STP)
报告时间：2026年7月18日上午10 : 30
地点：理工楼601
腾讯会议：481-209-819
报告摘要：Let $A$ be an $n\times n$ real matrix. As shown in the recent paper ``The bifurcation lemma for strong properties in the inverse eigenvalue problem of a graph'', Linear Algebra Appl. 648 (2022), 70--87, by S.M. Fallat, H.T. Hall, J.C.-H. Lin, and B.L. Shader, if the manifolds $ \{ G^{-1} A G : G\in \text{GL}(n, \mathbb R) \}$ and $Q(\text{sgn}(A))$ (consisting of all real matrices having the same sign pattern as $A$), both considered as embedded submanifolds of $\mathbb R^{n \times n}$, intersect transversally at $A$, then every superpattern of sgn$(A)$ also allows a matrix similar to $A$. Those authors say that the matrix $A$ has the nonsymmetric strong spectral property (nSSP) if $X = 0$ is the only matrix satisfying $A \circ X = 0$ and $AX^T - X^TA = 0, $ and show that the nSSP property of $A$ is equivalent to the above transversality. In this talk, this transversality property of $A$ is characterized using an alternative, more direct and convenient condition, called the similarity-transversality property (STP). Let $X=[x_{ij}]$ be a generic matrix of order $n$ whose entries are independent variables. The STP of $A$ is defined as the full row rank property of the Jacobian matrix of the entries of $AX-XA$ at the zero entry positions of $A$ with respect to the nondiagonal entries of $X$. This new approach makes it possible to take better advantage of the combinatorial structure of the matrix $A$, and provides theoretical foundation for constructing matrices similar to a given matrix while the entries have certain desired signs. Many results on matrices with the STP are presented. In particular, zero-nonzero patterns that allow the STP are characterized and important classes of zero-nonzero patterns and sign patterns that require the STP are identified. Examples illustrating many possible applications (such as diagonalizability, number of distinct eigenvalues, nilpotence, idempotence, semi-stability, the minimal polynomial, and rank) are provided. Several intriguing open problems are raised.
欢迎广大师生参加！
报告人简介
李忠善教授，现为美国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。1983年毕业于兰州大学数学专业，获理学学士；1986年毕业于北京师范大学数学专业，获理学硕士学位；1990年毕业于North Carolina（北卡罗来纳）州立大学数学专业，获理学博士学位。 自1991年起在美国乔治亚州立大学数学与统计系任教，1998年成为Georgia（佐治亚）州立大学副教授及终身教授，2007年晋升为正教授。2010年起担任数学系研究生部主任，并于2010年至2024年任佐治亚州立大学科学与艺术学院职称和终身教授评定委员会的成员。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。目前还担任美国《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。
甘肃省计算数学基础学科研究中心
数学与统计学院
萃英学院
2026年7月14日
