On the Stratiication of the Kronecker Canonical Form

The understanding of which Kronecker structures that are close to a given structure is revealed by the Kronecker structure hierarchy, i.e., the strati cation of the Kronecker canonical form. For a given matrix pencil A B, the Kronecker structure hierarchy shows all structures that are within the closure of orbit(A B), and each structure, whose orbit's closure contains A B. In order to gain new insight in the problem of strati cation, we give new interpretations of important results by Pokrzywa, for determining closure relations among orbits of Kronecker structures. This is partly done by generalizing classical theorems by Gantmacher. The results are used to derive an algorithm for computation of the complete Kronecker structure hierarchy, or the Kronecker structure hierarchy above or below a given structure. The algorithm is presented in terms of the rank-decisions required in a staircase algorithm, in order to compute the Kronecker structure hierarchy.