On the distance between lattices of invariant subspaces of matrices

Abstract

We study the behavior of the lattice Inv( X) of all invariant subspaces of a matrix X, when X belongs to the class of matrices with fixed Jordan structure (i.e., with isomorphic lattices of invariant subspaces). A larger class of matrices with fixed Jordan structure corresponding to the eigenvalues of geometric multiplicity greater than one is also studied. Our main concern is analysis of the distance between the lattices of invariant subspaces.