V2EX conrotatory

Conrotatory

Definition / 释义

(数学习语,尤指矩阵论)共旋的;共旋矩阵的。 通常指一种复矩阵性质:若复矩阵 \(A\) 满足
\[ A\,\overline{A}=-I \] (\(\overline{A}\) 为对 \(A\) 逐元素取复共轭,\(I\) 为单位矩阵),则称 \(A\) 为 conrotatory matrix(共旋矩阵)
注:该词非常少见,主要出现在特定的线性代数/矩阵论文献中。

Pronunciation / 发音(IPA)

/knrotetri/

Examples / 例句

This matrix is conrotatory.
这个矩阵是共旋的。

In the classification of complex matrices, conrotatory matrices satisfy \(A\overline{A}=-I\), which imposes a strong structural constraint.
在复矩阵的分类研究中,共旋矩阵满足 \(A\overline{A}=-I\),这会带来很强的结构性约束。

Etymology / 词源

con-(“共同、伴随”)+ rotatory(“旋转的”)。在相关数学语境里,con- 往往暗示与 complex conjugation(复共轭) 有关的“伴随/共轭”操作,因此该词常用于描述“与复共轭相结合的旋转式条件”(如 \(A\overline{A}=\pm I\) 这一类约束)。

Related Words / 相关汇

Notable Works / 文献与作品中的用例

  • Matrix Analysis Roger A. Horn & Charles R. Johnson(矩阵分析经典教材;相关术语常在矩阵分类与结构性质讨论中出现)
  • Topics in Matrix Analysis Roger A. Horn & Charles R. Johnson(延伸主题中更常涉及各类特殊矩阵性质术语)
  • Linear Algebra and Its Applications(期刊;关于特殊复矩阵与共轭约束条件的论文中可能出现该术语)
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