Inequalities: Theory of Majorization and Its Applications (Volume 143) (Mathematics in Science and Engineering, Volume 143) - Hardcover

Olkin, Ingram; Marshall, Albert W.

Hardcover

ISBN 10: 0124737501 ISBN 13: 9780124737501

Publisher: Academic Press, 1980

Synopsis

Although they play a fundamental role in nearly all branches of mathematics, inequalities are usually obtained by ad hoc methods rather than as consequences of some underlying "theory of inequalities." For certain kinds of inequalities, the notion of majorization leads to such a theory that is sometimes extremely useful and powerful for deriving inequalities. Moreover, the derivation of an inequality by methods of majorization is often very helpful both for providing a deeper understanding and for suggesting natural generalizations.Anyone wishing to employ majorization as a tool in applications can make use of the theorems; for the most part, their statements are easily understood.

About this title

Review

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)

From the Back Cover

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.

Edition details

• Publisher: Academic Press
• Publication date: 1980
• Language: English
• ISBN 10: 0124737501
• ISBN 13: 9780124737501
• Binding: Hardcover
• Number of pages: 569