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学术报告119:Dragan Rakic — Generalized inverses and space decompositions

时间:2022-11-07 作者: 点击数:

报告时间:2022年11月9日(星期三)16:00-18:00

报告地点:腾讯会议:708-347-376

:Dragan Rakic教授

工作单位:University of Nis

举办单位:学院

报告人简介:Dragan Rakic,塞尔维亚尼什大学教授,2015年博士毕业于尼什大学,主要研究方向为泛函分析、算子理论、广义逆及偏序理论。在专业杂志上等杂志上发表高质量论文20余篇,并主持塞尔维亚科学基金项目2项、及塞尔维亚与思罗维尼亚双边项目1项。

报告简介:For an arbitrary complex matrixA∈Cm×n, a generalized inverse (g-inverse) ofAis a matrixG∈Cn×mwhich satisfiesAGA=A.IfAis nonsingular thenA1is its only g-inverse, otherwise it has infinitely many g-inverses. Adding some more conditions we obtain specific g-inverses. Any matrix has unique Moore-Penrose and Drazin inverse and any matrixAfor which rankA= rankA2has unique group, core and dual core inverse. All of them can be defined by appropriate set of equations. Matrix decompositions such as singular value decomposition and Jordan decomposition enable us to obtain useful representations of these inverses. In the infinite dimensional case whenAis bounded linear operator acting on a Hilbert space we can not use these decompositions. Instead, every g-inverse induces corresponding space decompositions so we can obtain matrix representation of operator and its inverse. These representations are very useful tool in the study of g-inverses.

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