Advances in Applied Clifford Algebras

, Volume 9, Issue 1, pp 61–76 | Cite as

Similarity and consimilarity of elements in the real Cayley-Dickson algebras

  • Yongge Tian


The similarity and consimilarity of elements in the real quaternion, octonion and sedenion algebras, as well as in the general real Cayley-Dickson algebras are considered by solving the two fundamental equationsax=xb and\(ax = \bar xb\) in these algebras. Some consequences are also presented.

Key words and phrases

quaternions octonions sedenions equation similarity consimilarity square root 

AMS subject classifications

17A05 17A35 


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Copyright information

© Birkhäuser-Verlag AG 1999

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsConcordia UniversityMontréalCanada

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