四元数对合
Quaternion Involutions
摘要：
对合通常被定义为是其自身逆的映射。本文研究了四元数对合在加法和乘法上具有分布的附加性质。我们审查这样的对合的形式公理，我们表明，四元数有无限数量的对合。我们表明，共轭的四元数可以表示使用三个相互垂直的对合。我们还表明，任何一组三个相互垂直的四元数对合是封闭的组合。最后，我们证明了向量或四元数的投影可以用对合简明地表示。
英文摘要：
An involution is usually defined as a mapping that is its own inverse. In this paper, we study quaternion involutions that have the additional properties of distribution over addition and multiplication. We review formal axioms for such involutions, and we show that the quaternions have an infinite number of involutions. We show that the conjugate of a quaternion may be expressed using three mutually perpendicular involutions. We also show that any set of three mutually perpendicular quaternion involutions is closed under composition. Finally, we show that projection of a vector or quaternion can be expressed concisely using involutions.
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