an:00734901
Zbl 0815.15016
Berman, Abraham; Plemmons, Robert J.
Nonnegative matrices in the mathematical sciences
EN
Classics in Applied Mathematics. 9. Philadelphia, PA: SIAM,. xx, 340 p. (1994).
00418117
1994
b
15B48 15-02 65F10 15A30 15B51 60J10 90C33 93D25 15A18
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
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.
Eugene Seneta (Sydney)
Zbl 0278.15011; Zbl 0484.15016