Mathematics Graduate Students Organization

Seminar:

Date: February 24

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.