Berman, Abraham; Plemmons, Robert J. Nonnegative matrices in the mathematical sciences. (English) Zbl 0815.15016 Classics in Applied Mathematics. 9. Philadelphia, PA: SIAM,. xx, 340 p. (1994). This is a corrected soft-cover republication of the book first published in 1979 (Zbl 0484.15016). It has a new preface and a new chapter (Supplement 1979-1993, pp. 299-321) which includes 75 new references. The choice of new material reflects the personal interests and contacts of the authors; the new reference list accords with this. The subsections of the new chapter are:1. The Perron root and other eigenvalues [work on bounds and algorithms]. 2. The inverse eigenvalue problem. 3. Doubly nonnegative matrices [nonnegative matrices which are also nonnegative definite]. 4. Inverse nonnegative matrices. 5. Iterative methods and Markov chains. 6. Perron- Frobenius theory in a game of numbers. 7. Perron-Frobenius theory in nonnegative linear systems.An author index would have been a useful addition. Reviewer: Eugene Seneta (Sydney) Cited in 7 ReviewsCited in 1353 Documents MSC: 15B48 Positive matrices and their generalizations; cones of matrices 15-02 Research exposition (monographs, survey articles) pertaining to linear algebra 65F10 Iterative numerical methods for linear systems 15A30 Algebraic systems of matrices 15B51 Stochastic matrices 60J10 Markov chains (discrete-time Markov processes on discrete state spaces) 90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming) 93D25 Input-output approaches in control theory 15A18 Eigenvalues, singular values, and eigenvectors Keywords:doubly nonnegative matrices; inverse nonnegative matrices; iterative methods; invariant cone; inverse-positivity; \(M\)-matrices; input-output analysis; linear complementarity; Perron root; eigenvalues; inverse eigenvalue problem; Markov chains; nonnegative linear systems Citations:Zbl 0278.15011; Zbl 0484.15016 PDFBibTeX XMLCite \textit{A. Berman} and \textit{R. J. Plemmons}, Nonnegative matrices in the mathematical sciences. Philadelphia, PA: SIAM (1994; Zbl 0815.15016)