Ebook: Inequalities: Theory of Majorization and Its Applications

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.

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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.

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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.
Content:
Front Matter....Pages i-xxviii
Front Matter....Pages 1-1
Introduction....Pages 3-28
Doubly Stochastic Matrices....Pages 29-77
Schur-Convex Functions....Pages 79-154
Equivalent Conditions for Majorization....Pages 155-163
Preservation and Generation of Majorization....Pages 165-202
Rearrangements and Majorization....Pages 203-239
Front Matter....Pages 241-241
Combinatorial Analysis....Pages 243-267
Geometric Inequalities....Pages 269-296
Matrix Theory....Pages 297-365
Numerical Analysis....Pages 367-383
Front Matter....Pages 385-385
Stochastic Majorizations....Pages 387-440
Probabilistic, Statistical, and Other Applications....Pages 441-526
Additional Statistical Applications....Pages 527-574
Front Matter....Pages 575-575
Orderings Extending Majorization....Pages 577-609
Multivariate Majorization....Pages 611-633
Front Matter....Pages 635-635
Convex Functions and Some Classical Inequalities....Pages 637-692
Stochastic Ordering....Pages 693-756
Total Positivity....Pages 757-768
Matrix Factorizations, Compounds, Direct Products, and M-Matrices....Pages 769-782
Extremal Representations of Matrix Functions....Pages 783-795
Back Matter....Pages 797-909

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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.
Content:
Front Matter....Pages i-xxviii
Front Matter....Pages 1-1
Introduction....Pages 3-28
Doubly Stochastic Matrices....Pages 29-77
Schur-Convex Functions....Pages 79-154
Equivalent Conditions for Majorization....Pages 155-163
Preservation and Generation of Majorization....Pages 165-202
Rearrangements and Majorization....Pages 203-239
Front Matter....Pages 241-241
Combinatorial Analysis....Pages 243-267
Geometric Inequalities....Pages 269-296
Matrix Theory....Pages 297-365
Numerical Analysis....Pages 367-383
Front Matter....Pages 385-385
Stochastic Majorizations....Pages 387-440
Probabilistic, Statistical, and Other Applications....Pages 441-526
Additional Statistical Applications....Pages 527-574
Front Matter....Pages 575-575
Orderings Extending Majorization....Pages 577-609
Multivariate Majorization....Pages 611-633
Front Matter....Pages 635-635
Convex Functions and Some Classical Inequalities....Pages 637-692
Stochastic Ordering....Pages 693-756
Total Positivity....Pages 757-768
Matrix Factorizations, Compounds, Direct Products, and M-Matrices....Pages 769-782
Extremal Representations of Matrix Functions....Pages 783-795
Back Matter....Pages 797-909
....