 Dragana Cetkovic-Ilic: Various matrix equations and some specific classes of the solutions发布日期：2019-06-03  字号：大 中 小  【打印】

Dragana Cetkovic-Ilic 教授

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SCI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SCI杂志的审稿人。现受聘为湖北师范大学“磁湖学者”讲座教授。

We will  discuss the system of matrix equations AiXBi=Ci, 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 as R(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.

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