Totally Positive Matrices

This account of totally positive matrices treats their central properties with full proofs and a complete bibliography.

Totally positive matrices constitute a particular class of matrices that features strongly in many areas of mathematics with diverse applications. This account of the subject provides a comprehensive treatment of their central properties, with full proofs and a complete bibliography.Totally positive matrices constitute a particular class of matrices, the study of which was initiated by analysts because of its many applications in diverse areas. This account of the subject is comprehensive and thorough, with careful treatment of the central properties of totally positive matrices, full proofs and a complete bibliography. The history of the subject is also described: in particular, the book ends with a tribute to the four people who have made the most notable contributions to the history of total positivity: I. J. Schoenberg, M. G. Krein, F. R. Gantmacher and S. Karlin. This monograph will appeal to those with an interest in matrix theory, to those who use or have used total positivity, and to anyone who wishes to learn about this rich and interesting subject.