Abstract
Starting with a complex number \(z=a+bi\), and extending this to a quaternion \(q=[s+ai+bj+ck]\), it seems only natural to seek the existence of something similar with higher dimensions, which turns out to be an octonion, with eight elements. In this chapter I describe octonions, their algebraic properties and some worked examples. It is in no way a definitive exposition, but a gentle introduction to this obscure mathematical construct.
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References
Hurwitz A (1898) ber die Composition der quadratischen Formen von beliebig vielen Variabeln. Goett. Nachr. 309316
Cayley A (1845) On Jacobi’s elliptic functions, in reply to the Rev. B. Brownwin; and on quaternions. Philos. Mag. 26(1845):208–211
Baez JC http://www.math.ucr.edu/home/baez/octonions/node1.html
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Vince, J. (2018). Octonions. In: Imaginary Mathematics for Computer Science. Springer, Cham. https://doi.org/10.1007/978-3-319-94637-5_5
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DOI: https://doi.org/10.1007/978-3-319-94637-5_5
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