@article{George1999CommonIS,
title={Common invariant subspaces of two matrices},
author={A. George and K. Ikramov},
journal={Linear Algebra and its Applications},
year={1999},
volume={287},
pages={171-179}
}

Abstract A finite rational procedure of the Shemesh type is proposed to check whether given complex n × n matrices A and B have a common invariant subspace of dimension k , 2 ≤ k n . The only restriction is that at least one of A and B must have distinct eigenvalues. This fact can also be verified by a finite rational computation.