Nonnegative matrices in the mathematical sciences

Abraham Berman, Robert J. Plemmons9780898713213, 0898713218

Here is a valuable text and research tool for scientists and engineers who use or work with theory and computation associated with practical problems relating to Markov chains and queuing networks, economic analysis, or mathematical programming. Originally published in 1979, this new edition adds material that updates the subject relative to developments from 1979 to 1993. Theory and applications of nonnegative matrices are blended here, and extensive references are included in each area. You will be led from the theory of positive operators via the Perron-Frobenius theory of nonnegative matrices and the theory of inverse positivity, to the widely used topic of M-matrices.

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Table of contents :
Nonnegative Matrices in the Mathematical Sciences……Page 1
Contents……Page 8
Preface to the Classics Edition……Page 12
PREFACE……Page 14
ACKNOWLEDGMENTS……Page 18
SYMBOLS……Page 20
CHAPTER 1 MATRICES WHICH LEAVE A CONE INVARIANT……Page 22
CHAPTER 2 NONNEGATIVE MATRICES……Page 47
CHAPTER 3 SEMIGROUPS OF NONNEGATIVE MATRICES……Page 84
CHAPTER 4 SYMMETRIC NONNEGATIVE MATRICES……Page 108
CHAPTER 5 GENERALIZED INVERSE-POSITIVITY……Page 133
CHAPTER 6 M-MATRICES……Page 153
CHAPTER 7 ITERATIVE METHODS FOR LINEAR SYSTEMS……Page 186
CHAPTER 8 FINITE MARKOV CHAINS……Page 232
CHAPTER 9 INPUT-OUTPUT ANALYSIS IN ECONOMICS……Page 264
CHAPTER 10 THE LINEAR COMPLEMENTARITY PROBLEM……Page 292
CHAPTER 11 SUPPLEMENT 1979-19931……Page 320
REFERENCES……Page 343
INDEX……Page 358