I had been working with Complex Numbers and Quaternions and their Matrix Representation. Till now everything had been quite logical and it's easy to follow the extension from complex numbers to Quaternions. Now I have moved on to Octonions and the way Octonions Multiplication is defined itself doesn't seem to follow a pattern; it looks highly unintuitive to me. Can anyone explain why the Multiplication in Octonions is defined the way it is defined? Or is it that there is not pattern to understand and it is just that this definition works out for it to have a Structure like Division Algebra?
2026-04-02 20:54:26.1775163266
What is the intuition behind the multiplication defined for Octonions?
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