The Power Invariance Of Toeplitz Matrices And Sign Patterns

In this thesis we study the zero-pattern of nonnegative Toeplitz matrices and idem-potency of Toeplitz-type sign patterns. Our main results are as follows.1. We characterize the conditions for the zero-pattern invariant properties of nonneg-ative Toeplitz matrices, which cover the corresponding results by R. Huang and J. Liu.2. We discuss the idempotency of Toeplitz-type sign patterns and give an equivalent characterization for an irreducible Toeplitz-type sign pattern to be idempotent.