  A parametrization, given by the Euler angles, of Hermitian matrix generators
of even and odd-degenerate Clifford algebras is constructed by means of the
Kronecker product of a parametrized version of Pauli matrices and by the
identification of all possible anticommutation sets for a given algebra. The
internal parametrization of the matrix generators allows a straightforward
interpretation in terms of rotations, and in the absence of a similarity
transformation can be reduced to the canonical representations by an
appropriate choice of parameters. The parametric matrix generators of 2nd and
4th-order are linearly decomposed in terms of Pauli, Dirac, and 4th-order
Gell-Mann matrices establishing a direct correspondence between the bases. In
addition, and with the expectation for further applications in group theory, a
linear decomposition of GL(4) matrices on the basis of the parametric 4th-order
matrix generators and in terms of four-vector parameters is explored. By
establishing unitary conditions, a parametrization of two sub-groups of SU(4)
is achieved.
