Canonical forms for mixed symmetric-skewsymmetric quaternion matrix pencils (Q884420)

The author obtains canonical forms for pairs of quaternionic matrices which are mixed symmetric-skewsymmetric with respect to nonstandard involutory antiautomorphisms of the skew field of real quaternions, under strict equivalence and symmetry respecting congruences. In Section 2 the author recalls basic facts about the quaternionic algebra. Section 3 studies canonical forms for symmetric-skewsymmetric matrix pencils. In Section 4 the author develops some applications of the canonical form of Theorem 3.1. Section 5 presents another application of Theorem 3.1. In Section 6, the author addresses the canonical forms of skewsymmetric quaternionic linear transformations. Section 7 contains the proof of Theorem 3.1.