TY - GEN A1 - Mackey, D. Steven A1 - Mackey, Niloufer A1 - Mehl, Christian A1 - Mehrmann, Volker T1 - Jordan Structures of Alternating Matrix Polynomials N2 - Alternating matrix polynomials, that is, polynomials whose coefficients alternate between symmetric and skew-symmetric matrices, generalize the notions of even and odd scalar polynomials. We investigate the Smith forms of alternating matrix polynomials, showing that each invariant factor is an even or odd scalar polynomial. Necessary and sufficient conditions are derived for a given Smith form to be that of an alternating matrix polynomial. These conditions allow a characterization of the possible Jordan structures of alternating matrix polynomials, and also lead to necessary and sufficient conditions for the existence of structure-preserving strong linearizations. Most of the results are applicable to singular as well as regular matrix polynomials. KW - matrix polynomial KW - matrix pencil KW - structured linearization KW - Smith form KW - Jordan form KW - elementary divisor KW - invariant factor KW - invariant polynomial KW - alternating matrix polynomial KW - even/odd matrix polynomial Y1 - 2009 UR - https://opus4.kobv.de/opus4-matheon/frontdoor/index/index/docId/654 UR - https://nbn-resolving.org/urn:nbn:de:0296-matheon-6540 ER -