This book, "Non-negative Matrices and Markov Chains" by E. Seneta, is a comprehensive treatment of the theory of non-negative matrices and its applications in Markov chains. The second edition, published by Springer Science+Business Media, LLC, is a significant revision of the first edition published in 1973. The book aims to bridge the gap between pure mathematics and applied fields such as probability theory, numerical analysis, demography, mathematical economics, and dynamic programming. The content is divided into two parts: the first part focuses on finite non-negative matrices, while the second part develops an analogous theory for infinite matrices. The book is structured to be accessible to mathematicians and applied researchers, with a focus on real-variable methods. It includes detailed chapters on fundamental concepts, secondary theory, inhomogeneous products of non-negative matrices, Markov chains, and countable non-negative matrices. Key topics include the Perron-Frobenius theorem, irreducible matrices, ergodicity, and the practical computation of stationary distributions of infinite Markov chains. The book also introduces new sections and expansions, particularly in Chapters 2, 3, and 6, and includes exercises that complement the text. The author, E. Seneta, emphasizes the importance of understanding the theory from a non-negative matrix perspective and provides a detailed bibliography and index to support further study. The book is suitable for graduate students and researchers in various fields, offering a thorough and up-to-date treatment of the subject.This book, "Non-negative Matrices and Markov Chains" by E. Seneta, is a comprehensive treatment of the theory of non-negative matrices and its applications in Markov chains. The second edition, published by Springer Science+Business Media, LLC, is a significant revision of the first edition published in 1973. The book aims to bridge the gap between pure mathematics and applied fields such as probability theory, numerical analysis, demography, mathematical economics, and dynamic programming. The content is divided into two parts: the first part focuses on finite non-negative matrices, while the second part develops an analogous theory for infinite matrices. The book is structured to be accessible to mathematicians and applied researchers, with a focus on real-variable methods. It includes detailed chapters on fundamental concepts, secondary theory, inhomogeneous products of non-negative matrices, Markov chains, and countable non-negative matrices. Key topics include the Perron-Frobenius theorem, irreducible matrices, ergodicity, and the practical computation of stationary distributions of infinite Markov chains. The book also introduces new sections and expansions, particularly in Chapters 2, 3, and 6, and includes exercises that complement the text. The author, E. Seneta, emphasizes the importance of understanding the theory from a non-negative matrix perspective and provides a detailed bibliography and index to support further study. The book is suitable for graduate students and researchers in various fields, offering a thorough and up-to-date treatment of the subject.