报告时间：2019年6月5日（星期三）08:30-09:30

报告地点：翡翠科教楼B1710

报告人：DraganaCetkovic-Ilic教授

工作单位：University of Nis

报告人简介：主讲人简介：Dragana Cetkovic-Ilic，女，塞尔维亚尼什大学教授、博士生导师，2004年获得尼什大学博士学位，2010年获尼什大学终身教授，主要研究方向是算子广义逆理论及其应用。在Linear. Algebra. Appl.，Proc. Amer. Math. Soc.，Linear Multilinear Algebra，J. Austra. Math. Soc.，Acta Math. Sci.，Appl. Math. Comput.，J. Oper. Theory等杂志上发表高质量论文80余篇，2014年获得塞尔维亚数学会颁发的数学科学成就奖,现兼任Facta Universitatis, Filomat和Annals of Functional Analysis的编委和Acta Mathematica Hungarica, Mat. Vesnik, Publ. Inst. Math. Beograd, Filomat, J. Austra. Math. Soc.等多个高质量杂志的审稿人。现受聘为湖北师范大学“磁湖学者”讲座教授。

报告简介：We will discuss the system of matrix equations A_iXB_i=C_i, i= 1,4 and present some necessary and sufficient conditions for its solvability as well as an expression for the general solution. As corollaries we get generalizations of some recent results that involve solving some other systems of matrix equations. Also, we will consider the existence of a positive solution of the equation AXB=C was considered in different settings but only under additional conditions including that of regularity, as well as under certain range conditions such asR(B)⊆ R(A∗). In this talk we will answer this open question of the existence of a positive solution of the operator equation AXB=C without any additional range or regularity assumptions using two well-known results of Douglas and Zoltan. Also, we will give a general form of a positive solution and consider some possible applications.