为什么存在四元数和八元数

Q4 Mathematics Mathematics Magazine Pub Date : 2022-10-19 DOI:10.1080/0025570X.2022.2126252

F. Gould

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摘要

有一个简单的组合异常，使得一些特殊的线性代数成为可能，从而一些特殊的几何，只发生在维度1、2、4和8上。其结果是广泛的，特别是导致了复数、四元数和八元数的存在。本文用初等线性代数解释了为什么异常只存在于这些维度。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Why Quaternions and Octonions Exist

Summary There is a simple combinatorial anomaly, making possible some special linear algebra and thereby some special geometry, that occurs only in dimensions 1, 2, 4, and 8. The consequences are wide ranging and in particular lead to the existence of the complex numbers, the quaternions and the octonions. This article explains why the anomaly exists only in these dimensions using elementary linear algebra.

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