Inequalities : theory of majorization and its applications

Inequalities: Theory of Majorization and Its Applications; Preface and Acknowledgments from the First Edition; History and Preface of the Second Edition; Overview and Roadmap; Contents; Basic Notation and Terminology; Part I: Theory of Majorization; 1 Introduction; 2 Doubly Stochastic Matrices; 3 Schur-Convex Functions; 4 Equivalent Conditions for Majorization; 5 Preservation and Generation of Majorization; 6 Rearrangements and Majorization; Part II: Mathematical Applications; 7 Combinatorial Analysis; 8 Geometric Inequalities; 9 Matrix Theory; 10 Numerical Analysis.
Statisticians, probabilists, and mathematicians will all be interested in a expanded version of this classic work on inequalities. The theory of inequalities has applications in virtually every branch of mathematics.