V2EX pseudo-inverse

Pseudo-inverse

释义 Definition

伪逆(矩阵的伪逆):在线性代数中,对不一定可逆(如非方阵或奇异)的矩阵给出一种“广义逆”。最常见的是MoorePenrose 伪逆,常用于最小二乘拟合、求欠定/超定线性方程组的“最佳”解等。

发音 Pronunciation (IPA)

/sudo nvs/

例句 Examples

The pseudo-inverse helps solve least-squares problems.
伪逆有助于求解最小二乘问题。

When the matrix is singular, we can use the pseudo-inverse to compute a stable approximate solution.
当矩阵是奇异的时,我们可以用伪逆来计算一个稳定的近似解。

词源 Etymology

pseudo- 来自希腊语 pseudes(“假的、拟似的”),表示“类……但不完全是……”。inverse 源自拉丁语 inversus(“颠倒的、反转的”)。合起来 pseudo-inverse 字面意思是“拟似的逆”,指在不满足通常“可逆”条件时,仍定义一种具有逆的某些性质的运算对象。

相关词 Related Words

文学与经典著作中的用例 Literary Works

  • **Strang, Introduction to Linear Algebra**(线性代数教材中讨论伪逆与最小二乘)
  • **Golub & Van Loan, Matrix Computations**(矩阵计算经典著作,系统讲解 SVD 与伪逆)
  • **Trefethen & Bau, Numerical Linear Algebra**(数值线性代数中用伪逆解释最小二乘与稳定性)
  • **Ben-Israel & Greville, Generalized Inverses: Theory and Applications**(广义逆/伪逆专题经典)
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