Matrix positivity is a central topic in matrix theory: properties that generalize the notion of positivity to matrices arose from a large variety of applications, and many have also taken on notable theoretical significance, either because they are natural or unifying. This is the first book to provide a comprehensive and up-to-date reference of important material on matrix positivity classes, their properties, and their relations. The matrix classes emphasized in this book include the classes of semipositive matrices, P-matrices, inverse M-matrices, and copositive matrices. This self-contained reference will be useful to a large variety of mathematicians, engineers, and social scientists, as well as graduate students. The generalizations of positivity and the connections observed provide a unique perspective, along with theoretical insight into applications and future challenges. Direct applications can be found in data analysis, differential equations, mathematical programming, computational complexity, models of the economy, population biology, dynamical systems and control theory.

'When one thinks of positive matrices, usually only entrywise positive matrices and positive definite matrices come to mind. This book compiles results about an amazing array of 'positive' matrices beyond such familiar ones; semipositive matrices, inverse M-matrices and copositive matrices, to name a few. The treatment is lucid and a pleasure to read. Will facilitate anyone to widen the knowledge of matrix classes.'

R. B. Bapat - Indian Statistical Institute

'Positivity is one of the central topics in mathematics. Positivity of matrices is a rich and interesting research area of linear algebra and combinatorial matrix theory. Exhibiting many positivity classes of matrices with diligence, this monograph will be a very useful reference in research and applications.'

Fuzhen Zhang - Nova Southeastern University

‘Matrix Positivity is a reference work that will be useful not only to researchers and graduate students working in the area but also to readers who wish to find and apply results on matrix positivity to other areas of research.’

Brian Borchers Source: MAA Reviews

‘… this book is a good work on positive matrices and makes the travel through the untrodden path of inverseM-matrices and copositive matrices a smooth one.’

K. Premakumari Source: MathSciNet