Title：Generalized inverses, matrix and operator equations IV: Matrix and operator equations-solvability conditions and general forms

Abstract：Although solvability conditions for a system of two linear equations are well-known even in the case of rings and, for 3 linear equations, in the case of matrices, in the case of 4 linear equations there are no results. In this lecture we will consider systems of four linear matrix equations AiXBi =Ci, i = 1,2,3,4 and present certain necessary and sufficient conditions for their solvability as well as an expression for the general solution. There are two advantages to our results: the obtained solvability conditions can be in many cases presented in a purely algebraic form and the method used in the proof allows for a generalization of the obtained results to more general structures such as algebras of bounded linear operators or rings, under some additional assumptions concerning regularity only. We will present several applications of our results.

Speaker：Dragana S. Cvetković-Ilić，Department of Mathematics, Faculty of Science and Mathematics, University of Nis, Serbia

Dragana S. Cvetković-Ilić is a full professor of University of Nis, Serbia. Her main research field is the theory of generalized inverse and its applications. She has published more than 80 papers in SCI journals such as Linear Algebra Appl.，Proc. Amer. Math. Soc.，Linear & Multilinear Algebra，J. Austra. Math. Soc.，Acta Math. Sci.，Appl. Math. Comp.，J. Operator Theory and so on. She is a member of the Board of Directors of ILAS(International Linear Algebra Society), (3/2020-), member of the Editorial Board for the following journals: Journal of Computational and Applied Mathematics, Annals of Functional Analysis, FILOMAT, and FACTA UNIVERSITATIS, Series Mathematics and Informatics (Editor in Chief). She is also awarded by “For women in Sciences”, Loreal-Unesco, Serbia, and Award for achievements in Mathematical Sciences, Mathematical Society of Serbia.

Date：3:00pm-4:30pm 2021-4-23（Friday）.

Venue:

Tencent Meeting ID：168 475 022

Organizer：School of Mathematical Sciences

Students and teachers who are interested  are welcome.