منابع مشابه
Rényi divergence and majorization
Rényi divergence is related to Rényi entropy much like information divergence (also called Kullback-Leibler divergence or relative entropy) is related to Shannon’s entropy, and comes up in many settings. It was introduced by Rényi as a measure of information that satisfies almost the same axioms as information divergence. We review the most important properties of Rényi divergence, including it...
متن کاملGreed and Majorization
We present a straightforward linear algebraic model of greed, based only on extensions of classical majorization and convexity theory. This gives an alternative to other models of greedy-solvable problems such as matroids, greedoids, submodular functions, etc., and it is able to express established examples of greedy-solvable optimization problems that they cannot. The linear algebraic approach...
متن کاملCatalytic majorization and ` p norms
An important problem in quantum information theory is the mathematical characterization of the phenomenon of quantum catalysis: when can the surrounding entanglement be used to perform transformations of a jointly held quantum state under LOCC (local operations and classical communication) ? Mathematically, the question amounts to describe, for a fixed vector y, the set T (y) of vectors x such ...
متن کاملBalanced Words and majorization
Write |w| = m, the length of w, and |w|1 = card({1 ≤ i ≤ m : wi = 1}) its 1-length. Define the cyclic shift σ : {0, 1}m → {0, 1}m by σ(w1 . . . wm) = w2 . . . wmw1. A cyclic subword of w is any length-q prefix of some σi−1(w), 1 ≤ i, q ≤ m. To any word w = w1 . . . wm we associate its orbit O(w), the vector O(w) = (O1(w), . . . ,Om(w)) consisting of the iterated cyclic shifts w, σ(w), . . . , σ...
متن کاملLinear Preservers of Majorization
For vectors $X, Yin mathbb{R}^{n}$, we say $X$ is left matrix majorized by $Y$ and write $X prec_{ell} Y$ if for some row stochastic matrix $R, ~X=RY.$ Also, we write $Xsim_{ell}Y,$ when $Xprec_{ell}Yprec_{ell}X.$ A linear operator $Tcolon mathbb{R}^{p}to mathbb{R}^{n}$ is said to be a linear preserver of a given relation $prec$ if $Xprec Y$ on $mathbb{R}^{p}$ implies that $TXprec TY$ on $mathb...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematical Inequalities & Applications
سال: 2015
ISSN: 1331-4343
DOI: 10.7153/mia-18-76