Date: 24 Feb 2009

Computation of the eigenprojection of a nonnegative matrix at its spectral radius

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Abstract

In this paper we give a general representation for a projection in terms of its range and the range of its adjoint projection. By combining this representation with recent results of the author on the structure of the algebraic eigenspace of a nonnegative matrix corresponding to its spectral radius, we develop a computational method to find the cigenprojection of a nonnegative matrix at its spectral radius. The results are illustrated by giving a closed formula for computing the limiting matrix of a stochastic matrix.