报 告 人：Pedro Patricio 教授
工作单位：University of Minho, Portugal
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. He has 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.
报告简介： A von Neumann inverse of a matrix A is a solution to the matrix equation AXA=A. Although the row reduced echelon form allows to prove that any matrix over a field has a von Neumann inverse, a different approach has to be taken whilst considering matrices over a general (possibly non-commutative) ring. The Brown-McCoy Lemma comes to our help. In this talk, I will show that this lemma is a special case of some sort of orthogonality of matrices which delivers another method to construct a von Neumann inverse.