Computation of the eigenprojection of a nonnegative matrix at its spectral radius
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.
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- D. Gale, The theory of linear economic models (McGraw-Hill, New York, 1960).Google Scholar
- F. A. Graybill, Introduction to matrices with applications to statistics (Wadsworth Publishing Company, Inc., Belmont, Calif., 1969).Google Scholar
- S. Karlin, Mathematical methods and theory of games, programming, and economics, Vol. I (Addison-Wesley, Reading, Mass, 1959).Google Scholar
- H. Nikaido, Convex structure and economic theory (Academic Press, New York, 1968).Google Scholar
- U. G. Rothblum, “Multiplicative Markov decision chains”, Ph. D. Dissertation, Department of Operations Research, Stanford University, Stanford, Calif. (1974).Google Scholar
- U. G. Rothblum, “Expansions of sums of matrix powers and resolvents”, to appear.Google Scholar
- U. G. Rothblum and A. F. Veinott, Jr., “Average-overtaking cumulative optimality for polynomially bounded Markov decision chains”, to appear.Google Scholar
- R. S. Varga, Matrix iterative analysis (Prentice-Hall, Englewood Cliffs, N. J., 1962).Google Scholar