A parametrization, given by the Euler angles, of Hermitian matrix generators of even and odd non-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. 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 second and fourth-order are linearly decomposed in terms of Pauli, Dirac, and fourth-order Gell–Mann matrices establishing a direct correspondence between the different representations and matrix algebra 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 fourth-order matrix generators and in terms of four-vector parameters is explored. By establishing unitary conditions, a parametrization of two subgroups of SU(4) is achieved.

偶数和奇数非简并 Clifford 代数的 Hermitian 矩阵生成器的欧拉角给出的参数化是通过泡利矩阵参数化版本的克罗内克积以及所有可能的反交换集的识别来构造的。矩阵生成器的内部参数化允许在旋转方面进行直接解释，并且在没有相似变换的情况下可以通过适当选择参数将其简化为规范表示。二阶和四阶参数矩阵生成器根据泡利矩阵、狄拉克矩阵和四阶盖尔曼矩阵进行线性分解，在不同表示和矩阵代数基础之间建立直接对应关系。此外，为了在群论中进一步应用，探索了基于参数四阶矩阵生成器和四向量参数的 GL(4) 矩阵的线性分解。通过建立酉条件，实现了SU(4)的两个子群的参数化。