Matrix Positivity
Published on 1. October 2020
Book
Hardback
300 pages
978-1-108-47871-7 (ISBN)
Description
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.
Reviews / Votes
'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, 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, MathSciNetMore details
Series
Language
English
Place of publication
Cambridge
United Kingdom
Target group
Professional and scholarly
Product notice
sewn/stitched
Cloth over boards
Illustrations
Worked examples or Exercises
Dimensions
Height: 236 mm
Width: 161 mm
Thickness: 22 mm
Weight
489 gr
ISBN-13
978-1-108-47871-7 (9781108478717)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions
Charles R. Johnson
Matrix Positivity
E-Book
10/2020
Cambridge University Press
€93.99
Available for download
Charles R. Johnson | Ronald L. Smith | Michael J. Tsatsomeros
Matrix Positivity
E-Book
09/2020
Cambridge University Press
€100.99
Available for download
Persons
Charles R. Johnson is Class of 1961 Professor of Mathematics at College of William and Mary. He received his B.A. in mathematics and economics from Northwestern University in 1969 and his Ph.D. from The California Institute of Technology in 1972. He received tenure at the University of Maryland, College Park in 1976, had a brief professorship at Clemson University, and has been at College of William and Mary since 1987. He has had 13 PhD students, 6 Master's students, and involved more than 200 undergraduates in his research (steadily supported by NSF). Working in most parts of matrix analysis, and especially its interface with combinatorics, Professor Johnson has published nearly 500 papers and 15 books, and received several prizes.
Content
Background; 1. Positivity classes; 2. Semipositive matrices; 3. P-matrices; 4. Inverse M-matrices; 5. Copositive matrices.