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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.
List of contents
Introduction.- Doubly Stochastic Matrices.- Schur-Convex Functions.- Equivalent Conditions for Majorization.- Preservation and Generation of Majorization.- Rearrangements and Majorization.- Combinatorial Analysis.- Geometric Inequalities.- Matrix Theory.- Numerical Analysis.- Stochastic Majorizations.- Probabilistic, Statistical, and Other Applications.- Additional Statistical Applications.- Orderings Extending Majorization.- Multivariate Majorization.- Convex Functions and Some Classical Inequalities.- Stochastic Ordering.- TotalPositivity.- Matrix Factorizations, Compounds, Direct Products, and M-Matrices.- Extremal Representations of Matrix Functions.
About the author
Albert W. Marshall is Professor Emeritus of Statistics at the University of British Columbia. His fundamental contributions to reliability theory have had a profound effect in furthering its development.
Ingram Olkin is Professor Emeritus of Statistics at Stanford University. He has made fundamental contributions in multivariate analysis, and in the development of statistical methods in meta-analysis, which have resulted in its use in many applications.
Barry C. Arnold is Distinguished Professor of Statistics at the University of California, Riverside. His previous books deal with Pareto Distributions, Order Statistics, Record Values, Conditionally Specified Distributions, and the Lorenz Order.
Summary
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.
Additional text
From the reviews of the second edition:
“The second edition of the praised classic without whom I know that some people never leave home … . attempts to bring these uses to the fore so that the reader can see the extent and variation in its use. The chapters of the original version remain intact … . The bibliography has increased by over 50%. … Needless to say, the revised volume obviously continues as a celebrated classic.” (Simo Puntanen, International Statistical Review, Vol. 79 (2), 2011)
Report
From the reviews of the second edition:
"The second edition of the praised classic without whom I know that some people never leave home ... . attempts to bring these uses to the fore so that the reader can see the extent and variation in its use. The chapters of the original version remain intact ... . The bibliography has increased by over 50%. ... Needless to say, the revised volume obviously continues as a celebrated classic." (Simo Puntanen, International Statistical Review, Vol. 79 (2), 2011)
