Eventual properties of matrices
An eventual property of a matrix M is an element of C-nxn is a property that holds for all powers M-k, k >= k(0), for some positive integer k(0). Eventually positive and eventually nonnegative matrices have been studied extensively, and some results are known for eventually r-cyclic matrices. This paper introduces and establishs properties of eventually reducible matrices, establishs properties of the eigenstructure of eventually r-cyclic matrices, and answers affirmatively a question of Zaslavsky and Tam about eventually nonnegative matrices.
This article published as Hogben, Leslie, and Ulrica Wilson. "Eventual properties of matrices." The Electronic Journal of Linear Algebra 23 (2012): 953-965. DOI: 10.13001/1081-3810.1568. Posted with permission.