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词汇 Majorise
分类 英语词汇 英语翻译词典
释义

Majorise

英语百科

Majorization

（重定向自Majorise）
Figure 1. 2D Majorization Example
Figure 2. 3D Majorization Example

In mathematics, majorization is a preorder on vectors of real numbers. For a vector \mathbf{a}\in\mathbb{R}^d, we denote by \mathbf{a}^{\downarrow}\in\mathbb{R}^d the vector with the same components, but sorted in descending order. Given \mathbf{a},\mathbf{b} \in \mathbb{R}^d, we say that \mathbf{a} weakly majorizes (or dominates) \mathbf{b} from below written as \mathbf{a} \succ_w \mathbf{b} iff

where a^{\downarrow}_i and b^{\downarrow}_i are the elements of \mathbf{a} and \mathbf{b}, respectively, sorted in decreasing order. Equivalently, we say that \mathbf{b} is weakly majorized (or dominated) by \mathbf{a} from below, denoted as \mathbf{b} \prec_w \mathbf{a} .
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