Professor Seok-Zun Song
Department of Mathematics, Jeju University, Korea
An n × n matrix A is said to be primitive if Ak has all nonzero entries for some positive integer k. A primitive matrix A is said to have exponent k if Ak has all nonzero entries and As has a zero entry if s < k.
We consider the research history of exponents of primitive matrices and the subsets of primitive matrices with special exponents. We investigate linear preservers of these subsets of primitive matrices defined by their exponents. In particular, we shall characterize linear operators that preserve subsets with exponents 1 and 2, and those that preserve subsets with exponents n2 − 2n + 2 and n2 − 2n + 1. We also characterize those linear operators that strongly preserve subsets with exponents 2, n2 − 2n + 2 or n2 − 2n + 1.