Abstract
Let A be a finite square (reducible) nonnegative matrix. The main theorem of the paper gives first order approximations of f n ( A), for certain sequences f n of analytic functions. In particular, the theorem holds when f n ( A)= A n . The theorem is applied to study the local behavior of large powers of a nonnegative matrix, to study the limiting output vectors of a nonnegative multiplicative process, and to characterize the nonnegative eigenvectors of a nonnegative matrix. Finally, an application to absorbing Markov chains is given.
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