Inequalities: Theory of Majorization and Its ApplicationsElsevier Science, 28.12.1979 - 569 Seiten 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. |
Inhalt
B Majorization as a Partial Ordering | 12 |
Doubly Stochastic Matrices | 18 |
Doubly Substochastic Matrices and Weak Majorization | 24 |
Urheberrecht | |
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Inequalities: Theory of Majorization and Its Applications Ingram Olkin,Albert W. Marshall Eingeschränkte Leseprobe - 2016 |
Häufige Begriffe und Wortgruppen
a₁ a₂ argument b₁ c₁ characteristic roots column sums complex matrix components concave consequence convex cone convex functions convex hull D₁ Decreasing and Schur-convex denote density diagonal elements doubly stochastic matrix doubly substochastic equality equivalent examples exists finite number function defined functions g given h₁ Hadamard's inequality Hermitian matrix holds i₁ implies incidence matrix increasing inequality L-superadditive Lemma Littlewood Mirsky monotone n x n obtained Olkin P₁ permutation matrices Pólya positive definite positive semidefinite Proof Proposition Proschan prove r₁ random variables result follows row sums S₁ Schur Schur-concave function Schur-convex functions Section Sethuraman singular values strictly convex strictly Schur-convex Suppose symmetric and convex T-transforms t₁ Theorem tion triangles u₁ unitary unitary matrix vectors weak majorization x₁ y₁ yields α₁ Σ Σ