  Remarkably simple closed-form expressions for the elements of the groups
SU(n), SL(n,R), and SL(n,C) with n=2, 3, and 4 are obtained using linear
functions of biquaternions instead of n x n matrices. These representations do
not directly generalize to SU(n>4). However, the quaternion methods used are
sufficiently general to find applications in quantum chromodynamics and other
problems which necessitate complicated 3 x 3 or 4 x 4 matrix calculations.
