A criterion for the existence of common invariant subspaces of matrices Original Research Article

It is shown that square matrices A and B have a common invariant subspace W of dimension kgreater-or-equal, slanted1 if and only if for some scalar s, A+sI and B+sI are invertible and their kth compounds have a common eigenvector, which is a Grassmann representative for W. The applicability of this criterion and its ability to yield a basis for the common invariant subspace are investigated.