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The study of symmetries of partial differential equations (PDEs) has beentraditionally treated as a geometrical problem. Although geometrical methodshave been proven effective with regard to finding infinitesimal symmetrytransformations, they present certain conceptual difficulties in the case ofmatrix-valued PDEs; for example, the usual differential-operator representationof the symmetry-generating vector fields is not possible in this case. Analgebraic approach to the symmetry problem of PDEs is described, based onabstract operators (characteristic derivatives) which admit a standarddifferential-operator representation in the case of scalar-valued PDEs.

Infinitesimal symmetry transformations of matrix-valued differential equations: An algebraic approach