V2EX antisymmetric

Antisymmetric

释义 Definition

反对称的;反对称性(数学/物理):指在交换两个元素/变量的位置后,整体会变号或呈现相反关系的性质。常见于矩阵、关系与张量等语境中。
(注:在不同学科里具体定义略有差异,但核心是“交换 → 变号/相反”。)

发音 Pronunciation

/n.ta.smt.rk/

例句 Examples

An antisymmetric matrix satisfies \(A^{T} = -A\).
反对称矩阵满足 \(A^{T} = -A\)。

In quantum mechanics, the antisymmetric wavefunction of fermions ensures the Pauli exclusion principle.
在量子力学中,费米子的反对称波函数保证了泡利不相容原理。

词源 Etymology

antisymmetric 由 **anti-**(“反,对抗”)+ symmetric(“对称的”)构成,字面意思就是“反对称的”。在现代数学与物理术语中用于描述“交换后取相反(通常是取负号)”的结构特征。

相关词 Related Words

文学作品 Literary Works

  • 《量子力学原理》(The Principles of Quantum Mechanics) P. A. M. Dirac(讨论费米子与波函数的对称/反对称性质时常出现相关用法)
  • 《量子力学:非相对论理论》(Quantum Mechanics: Non-Relativistic Theory) L. D. Landau & E. M. Lifshitz(在多粒子体系与交换对称性语境中常见)
  • 《线性代数及其应用》(Linear Algebra and Its Applications) Gilbert Strang(涉及矩阵性质时会出现 antisymmetric/skew-symmetric 等术语)
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