Description
Book SynopsisThis 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.
Trade ReviewFrom 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)
Table of ContentsIntroduction.- 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.- Total Positivity.- Matrix Factorizations, Compounds, Direct Products, and M-Matrices.- Extremal Representations of Matrix Functions.
