Matrix Positivity

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. Ronald L. Smith is Professor Emeritus at the University of Tennessee, Chattanooga. He received his PhD in Mathematics at Auburn University, as well as an M.S. in Industrial Engineering at Auburn University and an M.S. in Mathematics at the University of California, Riverside. He taught at Northern Arizona State University for 4 years, and was Professor at University of Tennessee, Chattanooga for 35 years. Dr. Smith's research interests are linear algebra, graph theory, and matrix theory, with particular interest in nonnegative matrices and matrix completions. He received the Thomson-Reuters Original List of Highly Cited Researchers Award. The conference, “Recent Advances in Linear Algebra and Graph Theory” was held in his honour. Michael J. Tsatsomeros is Professor of Mathematics at Washington State University. He received his PhD in Mathematics at the University of Connecticut in 1990. He has held positions at the University of Victoria, University of Wisconsin–Madison, University of Regina, and the College of William and Mary, and has served as Professor at Washington State University since 2007. Professor Tsatsomeros has also served the International Linear Algebra Society in various capacities, including as a member of the Board of Directors, Advisory Committee, and Journal Committee. He is Co-Editor-In-Chief of the Electronic Journal of Linear Algebra and Associate Editor of Linear Algebra and Its Applications. His main area of research is nonnegative matrix theory and generalizations.

'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

• Background; 1. Positivity classes; 2. Semipositive matrices; 3. P-matrices; 4. Inverse M-matrices; 5. Copositive matrices.