报告一:The group inverse of a product

报告华体会（中国）-华体会（中国）：2018年6月5日（星期三）09:30-10:30

报告地点：翡翠科教楼B1710

报告人：Pedro Patricio 教授

工作单位：University of Minho

报告人简介：Prof.Pedro Patricio received his PhD degree inMathematics from University of Minho,Portugal in 2002. He is currently a Professorin Department of Mathematics and Applications, University ofMinho. He isthe Director of theCMAT-center of Mathematics,University ofMinho. His research interests includegeneralized inverses andpartial orders. He has published more than40 peer reviewed papers in leading journals includingLinear Algebra Appl., Linear Multilinear Algebra,Electron. J. Linear Algebra, andJ. Aust. Math. Soc.etc.

报告简介：The study of the group inverse of a product is not new. For example,

given a ring R, the group inverse of a triplet paq for which a∈ Rpa∩aqR was characterized by Puystjens-Hartwig (LAMA, 1997) and applied to the group inverse of a companion matrix. Here, we are interested in the group inverse of a product of two (von Neumann) regular ring elements, with no extra conditions.

报告二:On power bounded matrices

报告华体会（中国）-华体会（中国）：2018年6月5日（星期三）15：00-16:00

报告地点：翡翠科教楼B1710

报告人：Pedro Patricio 教授

工作单位：University of Minho

报告人简介：Prof.Pedro Patricio received his PhD degree inMathematics from University of Minho,Portugal in 2002. He is currently a Professorin Department of Mathematics and Applications, University ofMinho. He isthe Director of theCMAT-center of Mathematics,University ofMinho. His research interests includegeneralized inverses andpartial orders. He has published more than40 peer reviewed papers in leading journals includingLinear Algebra Appl., Linear Multilinear Algebra,Electron. J. Linear Algebra, andJ. Aust. Math. Soc.etc.

报告简介：A complex n by n matrix is power bounded when there is a

non-negative M such that the inequalities(A^k)_ij| ≤ M hold

for all i,j∈ {1,,,,,n} and k∈N.

I will address the general complex case with aid of the Jordan Form

and its spectral properties. In addition, a special canonical form is

used. I will then derive results for block triangular matrices, and

lastly,consider non-negative matrices.

I will start this talk revisiting properties of the minimal polynomial

of a matrix.

报告三:On crypto & coding: past, present and future (and the role of

generalized inverses)

报告华体会（中国）-华体会（中国）：2018年6月11日（星期二）09：00-10:00

报告地点：翡翠科教楼B1710

报告人：Pedro Patricio 教授

工作单位：University of Minho

报告人简介：Prof.Pedro Patricio received his PhD degree inMathematics from University of Minho,Portugal in 2002. He is currently a Professorin Department of Mathematics and Applications, University ofMinho. He isthe Director of theCMAT-center of Mathematics,University ofMinho. His research interests includegeneralized inverses andpartial orders. He has published more than40 peer reviewed papers in leading journals includingLinear Algebra Appl., Linear Multilinear Algebra,Electron. J. Linear Algebra, andJ. Aust. Math. Soc.etc.

报告简介：I will present some known results and algorithms concerning cryptography

and coding theory, mainly focused on their algebraic roots.

Title: On crypto & coding: past, present and future (quantum error

correction codes)

I will present the quantum counterpart of classical error correcting

codes, and the mathematical framework needed, constructing CSS codes

using known linear codes.

报告四:The Group Inverse of the Nivellateur

报告华体会（中国）-华体会（中国）：2018年6月12日（星期三）16：00-17:00

报告地点：翡翠科教楼B1710

报告人：Pedro Patricio 教授

工作单位：University of Minho

报告人简介：Prof.Pedro Patricio received his PhD degree inMathematics from University of Minho,Portugal in 2002. He is currently a Professorin Department of Mathematics and Applications, University ofMinho. He isthe Director of theCMAT-center of Mathematics,University ofMinho. His research interests includegeneralized inverses andpartial orders. He has published more than40 peer reviewed papers in leading journals includingLinear Algebra Appl., Linear Multilinear Algebra,Electron. J. Linear Algebra, andJ. Aust. Math. Soc.etc.

报告简介：The matrix equation AX−XB = C can be written in column form as Gvec(X) = vec(C).I will present necessary and sufficient conditions for the existence of

the group inverse of this matrix in terms of A and B, and provide

expressions for this group inverse.