报告 人：Pedro Patricio教授

工作单位：University of Minho

举办单位：数学学院

报告人简介：Prof. Pedro Patricio received his PhD degree in Mathematics from University of Minho, Portugal in 2002. He is currently a Professor in Department of Mathematics and Applications, University of Minho. He is the Director of the CMAT-center of Mathematics, University of Minho. His research interests include generalized inverses and partial orders in rings. He published more than 40 peer reviewed papers in leading journals including Linear Algebra Appl., Linear Multilinear Algebra,Electron. J. Linear Algebra, and J. Aust. Math. Soc. etc.

报告一:The Moore-Penrose inverse of von Neumann regular matrices over a ring

报告时间：2022年9月22日（星期四）20：00-21：00

报告地点：腾讯会议：931 726 159

报告简介：In this talk, I will present necessary and sufficient conditions for a von Neumann regular matrixAover an arbitrary ring, and also the matrices arising in certain factorizations ofAbe Moore-Penrose invertible.

报告二:About the von Neumann regularity of triangular block matrices

报告时间：2022年9月27日（星期二）20：00-21：00

报告地点：腾讯会议：483 486 730

报告简介：I will give Necessary and sufficient conditions for the von Neumann regularity of triangular block matrices with von Neumann regular diagonal blocks over arbitrary rings. Further, I will show the characterization of the von Neumann regularity of a class of triangular Toeplitz matrices over arbitrary rings. Some special results and a new algorithm are derived for triangular Toeplitz matrices over commutative rings. Finally, the Drazin invertibility of some companion matrices over arbitrary rings is considered, as an application.

报告三:The Moore-Penrose inverse of a factorization

报告时间：2022年9月30日（星期五）20：00-21：00

报告地点：腾讯会议：575 613 911

报告简介：We will present necessary and sufficient conditions for the product of matricesPAQto be Moore-Penrose invertible, whereAis von Neumann regular and there existPandQsuch thatP’PA=A=AQQ’. Finally, an application is given to matrices over separative regular rings.

报告四:Generalized invertibility in two semigroups of a ring

报告时间：2022年10月1日（星期六）20：00-21：00

报告地点：腾讯会议：479 133 466

报告简介：Given a regular elementtof a ringRwith unity 1, thenthas a group inverse if and only ifu = t²t^-+ 1-tt^-is invertible inRif and only ifv = t⁻t²+ 1-t^-tis invertible inR. There, a pertinent question whether the inverse ofuandvcould be directly related was posed. Similar equivalences appear in the characterization of Moore-Penrose and Drazin invertibility, and therefore analogous questions arise. We present a unifying result to answer these questions not only involving classical invertibility, but also some generalized inverses as well.

报告五:Drazin-Moore-Penrose invertibility in rings

报告时间：2022年10月7日（星期五）20：00-21：00

报告地点：腾讯会议：240 967 810

报告简介：Characterizations are given for elements in an arbitrary ring with involution, having a group inverse and a Moore-Penrose inverse that are equal and the difference between these elements and EP-elements is explained. The results are also generalized to elements for which a power has a Moore-Penrose inverse and a group inverse that are equal.

As an application, the ring of square matrices of ordermover a projective free ringRwith involution such thatR^mis a module of finite length, providing a new characterization for range-Hermitian matrices over the complexes.

报告六:Some additive results on Drazin inverses

报告时间：2022年10月11日（星期二）20：00-21：00

报告地点：腾讯会议：585 775 434

报告简介：In this talk, I will present some additive results on Drazin inverse of a sum of Drazin invertible elements. Some converse results are also presented.

报告七:On the Drazin index of regular elements

报告时间：2022年10月12日（星期三）20：00-21：00

报告地点：腾讯会议：373 641 388

报告简介：It is known that the existence of the group inversea^#of a ring elementais equivalent to the invertibility ofa²a^-+1-aa^-, independently of the choice of the von Neumann inversea^-ofa. We then relate the Drazin index ofato the Drazin index ofa²a^-+1-aa^-. We also give an alternative characterization when considering matrices over an algebraically closed field.

报告八:Moore-Penrose invertibility in involutory rings: the caseaa^†=bb^†.

报告时间：2022年10月18日（星期二）20：00-21：00

报告地点：腾讯会议：552 208 880

报告简介：Given two von Neumann regular elementsa,bin a general ring with an arbitrary involution, we shall present necessary and sufficient conditions toaa^†=bb^†. As a special case, we discuss EP elements.

报告九:The link between regularity and strong-pi-regularity

报告时间：2022年10月21日（星期五）20：00-21：00

报告地点：腾讯会议：885 543 124

报告简介：I will show that if all powers of a ring elementaare regular, thenais strongly pi-regular exactly when a suitable word in the powers ofaand their inner inverses is a unit.

报告十:The (2,2,0) Drazin inverse problem

报告时间：2022年10月25日（星期二）20：00-21：00

报告地点：腾讯会议：423 676 195

报告简介：In this talk, I will discuss the additive Drazin problem and the existence of the Drazin inverse of a two by two matrix with zero (2,2) entry.