The Roots of a Quaternion
The Roots of a Quaternion
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DOI：
10.1080/00029890.1942.11991248
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发表时间：
1942-06
影响因子：
0.5
通讯作者：
I. Niven
中科院分区：
文献类型：
--
作者：
I. Niven
四元数a的m次方根的存在性是已知的，* 因为这个问题归结为方程'“-o：= O的四元数根的存在性。我们被引导去询问有多少个m次根，以及如何找到它们。第一个问题的答案是，四元数a不是真实的数，它有m个不同的m次方根;如果a是真实的数，则有无穷多个m次方根，除非m= 2且a是正数，在这种情况下，只有两个平方根±Va。我们的证明方法给出了所有的根。
The existence of an mth root of a quaternion a is known,* since the question reduces to the existence of a quaternion root of the equation~'"-o:= O. We are led to inquire how many mth roots there are, and how to find them. The answer to the first inquiry is that there are exactly m distinct mth roots of a quaternion a which is not a real number; if a is real there are infinitely many mth roots unless m= 2 and a is positive, in which case there are only two square roots,±Va. Our method of proof gives all roots.