V2EX bidiagonal

Bidiagonal

释义 Definition

bidiagonal(双对角的):指一种矩阵结构除主对角线外,只在主对角线的上一条对角线下一条对角线(二者之一)可能还有非零元素,其余元素为零。常见于数值线性代数(如奇异值分解的中间步骤)。
(注:在更一般的用法中,也可指“与两条对角线相关的”。)

发音 Pronunciation (IPA)

/ba.da.n.l/

例句 Examples

A bidiagonal matrix has nonzero entries only on the main diagonal and one adjacent diagonal.
双对角矩阵只有主对角线和一条相邻对角线上可能出现非零元素。

In the SVD algorithm, a dense matrix is often first reduced to bidiagonal form to simplify later computations.
在奇异值分解算法中,稠密矩阵通常会先被化为双对角形式,以简化后续计算。

词源 Etymology

由 **bi-**(“二、双”)+ diagonal(“对角线的”)构成,字面意思就是“与两条对角线相关的”,在矩阵语境中特指“主对角线 + 一条相邻对角线”的结构。

相关词 Related Words

文学与经典著作 Notable Works

  • Matrix Computations Gene H. Golub, Charles F. Van Loan(讨论双对角化与相关数值算法)
  • Numerical Linear Algebra Lloyd N. Trefethen, David Bau III(涉及将矩阵化为双对角形式的思想与应用)
  • Linear Algebra and Its Applications Gilbert Strang(在线性代数与数值方法语境中提及相关矩阵结构)
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