V2EX rank-one

Rank-One

释义 Definition

“rank-one”(形容词)指秩为 1 的(常用于线性代数/矩阵/张量等语境);表示一个矩阵(或线性变换)只有一个线性独立的行/列方向,常可写成两个向量的外积形式。也可更泛指“仅有一个独立成分/自由度”的结构。

发音 Pronunciation (IPA)

/rk wn/

例句 Examples

This is a rank-one matrix.
这是一个秩为 1 的矩阵。

The method applies a rank-one update to refine the estimate without recomputing everything from scratch.
该方法使用秩一更新来改进估计,而无需从头重新计算全部内容。

词源 Etymology

“rank”源自表示“等级/序列”的词义,在数学里引申为“(矩阵的)秩”,即线性独立的维度数量;“one”表示数量 1。“rank-one”因此字面义为“秩为一”,在工程、统计与数值计算中常见,如“rank-one update(秩一更新)”“rank-one approximation(秩一近似)”。

相关词 Related Words

文学与著作 Notable Works

  • Matrix Computations(Golub & Van Loan)常见“rank-one update”等表述
  • Convex Optimization(Boyd & Vandenberghe)涉及低秩/秩一结构与相关推导
  • The Elements of Statistical Learning(Hastie, Tibshirani, Friedman)在统计学习与矩阵分解语境中出现秩一/低秩概念
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