Simple forms and invariant subspaces of H-expansive matrices

In this paper we consider a simple form for pairs of matrices (A,H)(A,H), where H is a real symmetric invertible matrix, and A is a real H  -expansive matrix, that is, ATHA−HATHA−H is positive semidefinite. For such pairs we use the simple form to give an explicit construction of real A-invariant maximal H-semidefinite subspaces.