A novel procedure for constructing invariant subspaces of a set of matrices

Abstract A problem that is frequently encountered in a variety of mathematical contexts to find the common invariant subspaces single or set matrices. new method proposed gives definitive answer this problem. The key idea consists finding eigenvectors for exterior powers matrices concerned. convenient formulation Plücker relations then used ensure these actually correspond provide initial constraints involving parameters. procedure computing divisors totally decomposable vector also provided. Several examples are given which calculations too tedious do by hand and performed coding conditions found into Maple. Our main motivation lies Lie symmetry, where adjoint representations symmetry algebra differential equation must be known explicitly comprehensively order determine all ideals algebra.