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.


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