Abstract
Abstract For a nonnegative matrix P, we discuss the relation of its marked reduced graph to that part of the Jordan form that is associated with the Perron-Frobenius root, to the nonnegativity of the eigenvectors and generalized eigenvectors, to the nonnegativity of solutions of linear equations, and to the asymptotic growth of powers of the matrix. Results are often stated in terms of M-matrices, and standard results on irreducible matrices are assumed. We give examples to illustrate the theorems surveyed.
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