Mathematical Physics


Quaternion Dynamics, Part 2 - Identities, Octonions, and Pentuples

Authors: Gary D. Simpson

This text develops various identities for Hamilton's quaternions. The results are presented in order of difficulty. Results are organized as Axioms, Vectors, Quaternions, and Matrices. There are also sections for Octonions and Pentuples. Axioms are presented first and are largely without rigorous proof. Subsequent identities are constructed from prior identities. When complex conjugates are discussed, the author's thinking is biased towards the original quaternion having a positive vector portion and the conjugate having a negative vector portion. To genuinely understand what is presented, it is recommended that the reader should visualize the concepts in addition to manipulating them algebraically. The algebra is certainly true, but the visual understanding is more elegant and intuitive. This text will likely be updated occasionally.

Comments: 39 Pages.

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Submission history

[v1] 2016-08-08 16:47:42

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