## Pedro Patricio: On power bounded matrices

：Pedro Patricio 教授

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.

A complex $n\times n$ matrix is power bounded - shortened to PB -  when there is a non-negative $M$ such that the inequalities $|(A^k)_{ij}| \le M$ hold  for all $i,j\in \{1,\dots,n\}$  and $k\in \mathbb{N}$. We will show that if $A$ is PB  then $I-A$ is group invertible. For the non-negative case, we will use the Frobenius Normal Form to characterize PB matrices.