Leiba Rodman, Topics in Quaternion Linear Algebra, Princeton Series in Applied Mathematics, Princeton University Press, Princeton, 2014, xii+363 pp, ISBN 978-0-691-16185-3 (hardback).

Abstract

The algebra H of quaternions, meaning the space R4 endowed with a nocommutative multiplication rule, was discovered by William Rowan Hamilton in 1844 (the notation H comes from his name). As it is known there only four possibilities to endow Rk with a multiplicative structure: k = 1 the real numbers, k = 2 the complex numbers, k = 4 the quaternions and k = 8 Cayley's algebra (or the octonions). The multiplication in H is noncommutative and in Cayley's algebra is noncommutative and nonassociative.