The main purpose of this paper is to study common invariant subspaces of any matrix in the centralizer of a given matrix A∈Mn(F), where F denotes an algebraically closed field. In particular, we obtain a necessary and sufficient condition for the existence of a common eigenvector for all the matrices in this set.
Magret, M. D.; Montoro, M. On the existence of a common eigenvector for all matrices in the commutant of a single matrix. "Linear algebra and its applications", Setembre 2012, vol. 437, núm. 5, p. 1285-1292.