Quaternions - Definitions

Helmut Knaust, Department of Mathematical Sciences, UTEP, El Paso TX 79968
hknaust@utep.edu
2/24/2012

A={{z,-w\[Conjugate]},{w,z\[Conjugate]}}

Here are the 4 basis elements:

ı=A/.{z->1,w->0}

i=A/.{z->0,w->1}

j=A/.{z->I,w->0}

k=A/.{z->0,w->I}

Hamilton's relations now hold:

{i.i==-ı,j.j==-ı,k.k==-ı,
i.j==k,j.k==i,k.i==j,
j.i==-k,k.j==-i,i.k==-j}