Basic Classes of Matrices With Respect To Quaternionic Indefinite Inner Product Spaces
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.
D. Alpay, A, Ran and L. Rodman. Basic classes of matrices with respect to quaternionic indefinite inner product spaces. Linear Algebra and its Applications, vol. 416 (2006) pp. 242-269.