Inequalities: Theory of Majorization and Its ApplicationsAcademic Press, 28 de juny 2014 - 569 pàgines 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. |
Continguts
Mathematical Applications | 169 |
Stochastic Applications | 279 |
Generalizations | 415 |
Complementary Topics | 441 |
Biographies | 521 |
| 531 | |
Author Index | 553 |
| 559 | |
Altres edicions - Mostra-ho tot
Inequalities: Theory of Majorization and Its Applications Albert W. Marshall,Ingram Olkin Visualització de fragments - 1979 |
Frases i termes més freqüents
argument characteristic roots column sums components consequence convex cone convex function convex hull definite Hermitian matrices denote density diagonal elements distribution functions doubly stochastic matrix doubly substochastic equality equivalent examples exchangeable random variables exists function defined functions g given Hermitian matrix holds implies incidence matrix indicator function inequality L-superadditive Lemma Let X1 linear Littlewood m x n Math Mirsky monotone multinomial distribution n x n complex matrix n x n Hermitian matrix n x n matrix obtained Olkin permutation matrices Pólya positive definite positive definite Hermitian positive semidefinite positive semidefinite Hermitian Proposition Proschan prove random vectors result follows row sums satisfy Schur Schur-concave function Schur-convex function Section Sethuraman Similarly singular values strictly convex strictly Schur-convex Suppose symmetric and convex T-transforms Theorem tion triangles unitary matrix weak majorization yields