Apress Access

Inequalities: Theory of Majorization and Its Applications

By Albert W. Marshall , Ingram Olkin , Barry C. Arnold

  • eBook Price: $99.00
Buy eBook Buy Print Book

Inequalities: Theory of Majorization and Its Applications Cover Image

The theory of inequalities has applications in virtually every branch of mathematics. This revised and expanded edition of a classic work on inequalities will be of interest to statisticians, probabilists, and mathematicians.

Full Description

  • Add to Wishlist
  • ISBN13: 978-0-3874-0087-7
  • 937 Pages
  • Publication Date: November 25, 2010
  • Available eBook Formats: PDF
Full Description
This book’s first edition has been widely cited by researchers in diverse fields. The following are excerpts from reviews. “Inequalities: Theory of Majorization and its Applications” merits strong praise. It is innovative, coherent, well written and, most importantly, a pleasure to read. … This work is a valuable resource!” (Mathematical Reviews). “The authors … present an extremely rich collection of inequalities in a remarkably coherent and unified approach. The book is a major work on inequalities, rich in content and original in organization.” (Siam Review). “The appearance of … Inequalities in 1979 had a great impact on the mathematical sciences. By showing how a single concept unified a staggering amount of material from widely diverse disciplines–probability, geometry, statistics, operations research, etc.–this work was a revelation to those of us who had been trying to make sense of his own corner of this material.” (Linear Algebra and its Applications). This greatly expanded new edition includes recent research on stochastic, multivariate and group majorization, Lorenz order, and applications in physics and chemistry, in economics and political science, in matrix inequalities, and in probability and statistics. The reference list has almost doubled.
Table of Contents

Table of Contents

  1. Introduction.
  2. Doubly Stochastic Matrices.
  3. Schur
  4. Convex Functions.
  5. Equivalent Conditions for Majorization.
  6. Preservation and Generation of Majorization.
  7. Rearrangements and Majorization.
  8. Combinatorial Analysis.
  9. Geometric Inequalities.
  10. Matrix Theory.
  11. Numerical Analysis.
  12. Stochastic Majorizations.
  13. Probabilistic, Statistical, and Other Applications.
  14. Additional Statistical Applications.
  15. Orderings Extending Majorization.
  16. Multivariate Majorization.
  17. Convex Functions and Some Classical Inequalities.
  18. Stochastic Ordering.
  19. Total Positivity.
  20. Matrix Factorizations, Compounds, Direct Products, and M
  21. Matrices.
  22. Extremal Representations of Matrix Functions.

If you think that you've found an error in this book, please let us know by emailing to editorial@apress.com . You will find any confirmed erratum below, so you can check if your concern has already been addressed.
No errata are currently published


    1. PHP Objects, Patterns, and Practice


      View Book

    2. Beginning Android 3D Game Development


      View Book

    3. Troubleshooting Oracle Performance


      View Book

    4. Beginning Amazon Web Services with Node.js


      View Book