Date: 24 Feb 2009

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

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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.

Parts of the research reported in this paper are based on the author’s Ph.D. dissertation submitted to the Department of Operations Research at Stanford University. Research at Stanford University was supported by NSF Grant GK-18339 and ONR Contract N00014-67-A-0112-0050. Further research at the Courant Institute was supported by NSF Grant GP-37069.
My deepest thanks are given to my teacher and advisor, Professor Arthur F. Veinott, Jr., for his guidance and advice, for his insight and perspective, during the preparation of my Ph.D. dissertation.