V2EX block diagonal matrix

Block Diagonal Matrix

释义 Definition

块对角矩阵:一种矩阵,经过把行列按“块(block)”分组后,只有主对角线上的若干子矩阵(块)可能是非零的,而对角线以外的块通常为零矩阵。它常用来表示“彼此独立/不耦合”的子系统或把大问题分解成多个小问题来计算。

发音 Pronunciation (IPA)

/blk danl metrks/

例句 Examples

A block diagonal matrix is easy to invert if each block is invertible.
如果每个块都可逆,那么块对角矩阵就很容易求逆。

After reordering the basis vectors, the linear operator can be represented by a block diagonal matrix, revealing two independent subspaces with different eigenvalue structures.
在重新排列基向量之后,该线性算子可以用块对角矩阵表示,从而揭示出两个相互独立的子空间,并且它们具有不同的特征值结构。

词源 Etymology

block 原义为“块、分块”,在数学里引申为“把矩阵按子矩阵分区”;diagonal 来自“对角线”的概念;matrix 来自拉丁语 matrix(“母体/源头”之意),在数学中指承载数据或线性变换的“矩阵”。三者组合成术语,字面意思就是“由若干块组成、且这些块位于对角线上的矩阵”。

相关词 Related Words

文学/名著用例 Literary Works

  • Sheldon Axler, Linear Algebra Done Right(线性代数教材中常用块对角形式来表达直和分解与不变子空间思想)
  • Roger A. Horn & Charles R. Johnson, Matrix Analysis(矩阵分析经典著作,讨论分块矩阵、相似变换与块对角化相关主题)
  • Gene H. Golub & Charles F. Van Loan, Matrix Computations(数值线性代数名著,块对角结构常用于高效计算与分解算法的描述)
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