V2EX toeplitz

Toeplitz

释义 Definition

Toeplitz(托普利兹)通常指Toeplitz 矩阵/算子:一种矩阵结构,特点是每一条从左上到右下的对角线(主对角线及其平行对角线)上的元素都相同。它在信号处理、时间序列、卷积、数值线性代数等领域很常见。(也可作形容词用:a Toeplitz matrix

发音 Pronunciation (IPA)

/tplts/

例句 Examples

A Toeplitz matrix has constant values along each diagonal.
托普利兹矩阵的每条对角线上的数值都保持不变。

In signal processing, Toeplitz matrices often arise when a convolution is written as a linear system.
在信号处理中,把卷积写成线性方程组时,经常会自然出现托普利兹矩阵。

词源 Etymology

Toeplitz源自人名,来自德国数学家 Otto Toeplitz(奥托托普利兹,18811940);这一类矩阵与相关理论因其研究与推广而以他命名,属于“以学者姓名命名的数学术语”。

相关词 Related Words

文学与著作中的用例 Literary Works

  • Gray, R. M. Toeplitz and Circulant Matrices: A Review(系统综述 Toeplitz/循环矩阵的经典文献)
  • Horn & Johnson Matrix Analysis(矩阵分析权威教材,涉及 Toeplitz 等结构矩阵与相关性质)
  • Gilbert Strang Introduction to Linear Algebra(线性代数教材中常在结构矩阵、卷积/差分等语境提到 Toeplitz)
  • Grenander & Szeg Toeplitz Forms and Their Applications(Toeplitz 型(Toeplitz forms)与应用的经典专著)
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