Pairs of Hermitian and skew-Hermitian quaternionic matrices: canonical forms and their applications
The author describes canonical forms and their applications for pairs of Hermitian and/or skew-Hermitian quaternionic matrices. The paper is mainly expository, and most of the results here are not new, although some applications, corollaries, and auxiliary results perhaps have not been previously observed. 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-selfadjoint 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.
scientific article; zbMATH DE number 5307045
scientific article