V2EX skew-symmetric

Skew-symmetric

Definition 定义

(数学)反对称的;斜对称的。 常见于线性代数中:若方阵 \(A\) 满足 \(A^{T} = -A\),则称 \(A\) 为skew-symmetric(反对称)矩阵。(在更一般的语境中,也可指“反对称的”结构或形式。)

Pronunciation 发音

/skju smtrk/

Examples 例句

A skew-symmetric matrix has zeros on its diagonal.
反对称矩阵的主对角线元素都是 0。

Because \(A^T=-A\), the quadratic form \(x^T A x\) is always zero for any real vector \(x\) when \(A\) is skew-symmetric.
因为 \(A^T=-A\),当 \(A\) 为反对称矩阵时,对任意实向量 \(x\),二次型 \(x^T A x\) 恒为 0。

Etymology 词源

skew- 表示“倾斜的、偏斜的”,在数学里引申为“相对常规对称有所偏离/取负”的关系;symmetric 来自希腊语 symmetria(“对称、匀称”)。合起来 skew-symmetric 指一种“以转置为镜像时变为相反数”的“反向对称”。

Related Words 相关词

Literary Works 出现于哪些著作

  • 《Linear Algebra and Its Applications》(Gilbert Strang,《线性代数及其应用》)
  • 《Introduction to Linear Algebra》(Gilbert Strang,《线性代数导论》)
  • 《Linear Algebra Done Right》(Sheldon Axler,《线性代数应该这样学》)
  • 《Matrix Analysis》(Roger A. Horn & Charles R. Johnson,《矩阵分析》)
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