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Octonion

Numbers with eight dimensions are called octonions. You write them as

w = a + bi + cj + dk + ep + fq + gr + hs

and consists of the real numbers a, b, c, d, e, f, g and the units i, j, k, p, q, r, s. The set of octonions is indicated by the symbol O.

 


Explanation

When multiplying the units i, j, k, p, q, r, s the order plays a role.

1 i j k p q r s
i −1 k −j q −p −s r
j −k −1 i r s −p −q
k j −i  −1 s −r q −p
p −q −r −s  −1 i j k
q p −s r −i  −1 −k j
r s p −q −j k  −1 −i
s −r q p −k −j i  −1

 


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