V2EX submatrix

Submatrix

定义 Definition

子矩阵:从一个较大的矩阵中,选取某些行和某些列(通常保持原有顺序)所形成的较小矩阵。常用于线性代数、数值计算与统计学中(如主子矩阵、块矩阵的子块等)。

发音 Pronunciation (IPA)

/sbmetrks/

例句 Examples

A submatrix is formed by deleting some rows and columns from a matrix.
子矩阵可以通过从原矩阵中删除若干行和若干列得到。

To compute the determinant by expansion, we often use minors that come from specific submatrices.
用展开法计算行列式时,常会用到由特定子矩阵产生的余子式(minor)。

词源 Etymology

sub- 表示“下级的、部分的”,matrix 表示“矩阵”。合起来字面意思就是“矩阵的一个部分”,在数学语境中专指从原矩阵截取出来的较小矩阵。

相关词 Related Words

文学与著作中的用例 Literary Works

  • Gilbert Strang, Introduction to Linear Algebra(线性代数教材中常在“子矩阵/主子矩阵/块矩阵”相关章节出现)
  • Roger A. Horn & Charles R. Johnson, Matrix Analysis(矩阵分析经典著作,讨论主子矩阵、子矩阵与特征值性质等)
  • Gene H. Golub & Charles F. Van Loan, Matrix Computations(数值线性代数中涉及从大矩阵抽取子矩阵进行分解与计算)
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