In this section we continue to study the indecomposable matrix pairs adopting the same notation as in part I of this paper.

If the matrix A is regular and if it is symmetric or anti-symmetric such that

3.1

and if the matrix pair (X, A) is indecomposable then the corresponding representation space either is indecomposable or it is the direct sum of two indecomposable invariant subspaces. These are operator isomorphic if and only if the minimal polynomial mX of X is equal to (x-δ)μ where

3.2

at any rate there is even a decomposition of the representation space into the direct sum of two isotropic indecomposable invariant subspaces provided the characteristic of F is not 2.