V2EX tensor

Tensor

释义 Definition

Tensor(张量):一种数学对象,用来描述多维数据及其在坐标变换下的关系。通俗地说,标量是“一个数”,向量是“一列数”,矩阵是“二维表”,张量则可推广到“三维及以上的数组/结构”,常见于物理学、工程学与机器学习中。(注:在更严格的数学里,张量不只是“多维数组”,还强调其变换性质。)

发音 Pronunciation (IPA)

/tn.s/

例句 Examples

A tensor can represent a color image as height × width × channels.
张量可以把彩色图像表示为“高 × 宽 × 通道数”。

In general relativity, the curvature of spacetime is described using tensors that remain meaningful under changes of coordinates.
在广义相对论中,时空的曲率用张量来描述,它在坐标变化下仍保持明确的物理意义。

词源 Etymology

tensor 来自拉丁语 tendere(“拉、伸展”),与 “tension(张力)”同源。它最早在数学与物理语境中被用来表达“拉伸/应力等相关量的关系结构”,后来扩展为现代线性代数与物理学中的“张量”概念。

相关词 Related Words

文学与名著用例 Literary Works

  • Albert Einstein, Relativity: The Special and the General Theory(相对论科普著作中涉及张量思想与相关表述,常以“张量/张量分析”语境出现)
  • James Clerk Maxwell, A Treatise on Electricity and Magnetism(电磁理论中讨论场与应力等概念的数学表达,与张量语言密切相关)
  • Hermann Weyl, SpaceTimeMatter(系统讨论相对论与几何方法,张量作为核心工具频繁出现)
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