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Erschienen in:
2007 | OriginalPaper | Buchkapitel
Canonical Forms for Symmetric and Skewsymmetric Quaternionic Matrix Pencils
verfasst von : Leiba Rodman
Erschienen in: System Theory, the Schur Algorithm and Multidimensional Analysis
Verlag: Birkhäuser Basel
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Canonical forms are given for pairs of quaternionic matrices, or equivalently matrix pencils, with various symmetry properties, under strict equivalence and symmetry respecting congruence. Symmetry properties are induced by involutory antiautomorphisms of the quaternions which are different from the quaternionic conjugation. Some applications are developed, in particular, canonical forms for quaternionic matrices that are symmetric or skewsymmetric with respect to symmetric or skewsymmetric quaternion-valued inner products. Another application concerns joint numerical cones of pairs of skewsymmetric quaternionic matrices.