V2EX block diagonal

Block Diagonal

Definition / 释义

block diagonal(多用于数学/线性代数/计算):指“块对角的;块对角矩阵的”。在矩阵中,只有若干个“方块”(子矩阵)沿主对角线排列,其他位置通常为零(或空白),从而便于分解与计算。也常见名词用法:block diagonal matrix(块对角矩阵)。

Pronunciation / 发音(IPA)

/blk danl/

Examples / 例句

The matrix is block diagonal.
这个矩阵是块对角的。

By permuting the basis vectors, we can rewrite the operator in a block diagonal form, which makes the eigenvalue computation much easier.
通过重新排列基向量,我们可以把该算子改写成块对角形式,从而使特征值计算容易得多。

Etymology / 词源

block 原意为“块、区块”,diagonal 意为“对角线的”。合在一起用于矩阵语境时,强调“由若干子块沿对角线排列”的结构特征;该术语随现代线性代数与数值计算的发展而广泛固定下来。

Related Words / 相关词

Literary Works / 文献与著作中的用例

  • Matrix Analysis(Roger A. Horn, Charles R. Johnson)
  • Matrix Computations(Gene H. Golub, Charles F. Van Loan)
  • Linear Algebra and Its Applications(Gilbert Strang)
  • Linear Algebra Done Right(Sheldon Axler)
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