Chapter 10

Nonnegative Matrices and Stochastic Matrices

Uriel G. Rothblum

Technion

Nonnegativity is a natural property of many measured quantities (physical and virtual). Consequently, nonnegative matrices arise in modelling transformations in numerous branches of science and engineering — these include probability theory (Markov chains), population models, iterative methods in numerical analysis, economics (input-output models), epi–demiology, statistical mechanics, stability analysis, and physics. This chapter is concerned with properties of such matrices. The theory of the subject was originated in the pioneering work of Perron and Frobenius in [Per07a, Per07b, Fro08, Fro09, and Fro12]. There have been books, chapters in books, and hundreds ...

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