Basic classes of matrices or linear transformations in finite dimensional quaternionic vector spaces with a regular indefinite inner product are introduced and studied. The classes include plus matrices, selfadjoint, skew-adjoint, and unitary matrices. In particular, results are proved concerning extensions of invariant semidefinite subspaces. Canonical form for unitary matrices is developed and subsequently applied to stability of periodic Hamiltonian systems.
- Canonical forms
- Indefinite inner product
- Invariant semidefinite subspaces
- Plus matrix
- Quaternionic vector space