Q for quaternions

Extract

Quaternions feature in most introductory textbooks on abstract algebra, often in the form of exercises. They offer an important example of a skew field (or division ring); the subset of quaternions ±i, ±j, ±k, ±l (or ±I, ±J, ±K, ±L according to taste) under multiplication affords an example of the ‘awkward’ group of order 8, which is often known as the quaternion group; they have a convenient representation in the form of matrices, which provides the work with a computational foundation; and, for those who like that kind of thing, they can be introduced as ordered quadruples of real numbers with prescribed laws for addition and multiplication, on lines similar to the number-pair approach to integers, rationals and complex numbers.