## Seminar:

Spring 2014, Thursdays, Blocker 113, 4:00-4:50 PM
__ Date:__ ** February 24 **

**" Eventually Properties of Matrices "**

**Dr. Ulrica Wilson**

__Abstract__An eventual property of a matrix $M\in\mathbb{C}^{n\times n}$ is a property that holds for all powers $M^k, k\ge k_0$, for some positive integer $k_0$. Eventually positive and eventually nonnegative matrices have been studied extensively since their introduction by Friedland in 1978. Eventually positive matrices are characterized by Perron-Frobenius properties and while there is no such characterization for eventually nonnegative matrices, there is much that can be said. For instance there is a subclass of eventually nonnegative matrices called strongly eventually nonnegative matrices that have nice characterizations. Eventually $r$-cyclic matrices were introduced to study SEN matrices. In this talk we discuss the spectral structure of eventually $r$-cyclic matrices and some other eventual properties of matrices.