quaternion,
n.a generalized complex number, x, consisting of four components such that
x = x0 + x1i + x2j + x3k,
where the xi are real numbers and i, j, k are hypercomplex numbers for which
i2 = j2 = k2 = ijk = -1
The set of all quaternions is denoted by IH, and forms a division ring (a skew field).
The quaternion group is the set
{ ±1, ±i, ±j, ±k }
with respect to the multiplication of the unit quaternions.