V2EX finite-rank

Finite-rank

释义 Definition

(数学/线性代数/泛函分析)有限秩的:指矩阵或线性算子(operator)的秩(rank)是有限的,也就是其值域(image)的维数有限。常见搭配:finite-rank operator(有限秩算子)。

发音 Pronunciation (IPA)

/fanat rk/

例句 Examples

This matrix is finite-rank.
这个矩阵是有限秩的。

Every finite-rank operator on a Hilbert space is compact, and can be written as a finite sum of rank-one operators.
希尔伯特空间上的每个有限秩算子都是紧算子,并且可以写成有限个秩一算子的和。

词源 Etymology

finite(有限的)+ rank(秩、等级)构成的复合形容词。这里的 rank 来自线性代数中的“秩”,表示线性变换(或矩阵)所能“覆盖”的独立方向数量;加上 finite 强调这个数量是有限的。

相关词 Related Words

文学与著作 Literary Works

  • A Course in Functional Analysis(John B. Conway)
  • Functional Analysis(Walter Rudin)
  • Introductory Functional Analysis with Applications(Erwin Kreyszig)
  • Methods of Modern Mathematical Physics, Vol. I: Functional Analysis(Reed & Simon)
  • Functional Analysis(Peter D. Lax)
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