# Quaternions

Formulated by the Irish Mathematician Sir William Rowan Hamilton in 1843, the quaternions are an extension of complex numbers $z=a+ib$ into four dimensions to form $z=a+bi+cj+dk$ where $i^2=j^2=k^2=ijk=-1.$
Multiplication of quaternions does not necessarily commute - note that $ij=-ji$ . The algebra of Quaternions was one of the first non-commutative algebras to be devised.