Pairs of hermitian and skew-hermitian quaternionic matrices: Canonical forms and their applications

Canonical forms are described for pairs of quaternionic matrices, or equivalently matrix pencils, where each one of the matrices is either hermitian or skew-hermitian, under strict equivalence and simultaneous congruence. Several applications are developed, including structure of selfadjoint and skew-adjoint matrices with respect to a regular sesquilinear quaternion valued form, or with respect to a regular skew-sesquilinear form. Another application gives canonical forms for quaternionic matrices under congruence.