TY - GEN A1 - Mackey, D. Steven A1 - Mackey, Niloufer A1 - Mehl, Christian A1 - Mehrmann, Volker T1 - Möbius Transformations of Matrix Polynomials N2 - We discuss Möbius transformations for general matrix polynomials over arbitrary � elds, analyzing their in uence on regularity, rank, determinant, constructs such as compound matrices, and on structural features including sparsity and symmetry. Results on the preservation of spectral information contained in elementary divisors, partial multiplicity sequences, invariant pairs, and minimal indices are presented. The e� ect on canonical forms such as Smith forms and local Smith forms, on relationships of strict equivalence and spectral equivalence, and on the property of being a linearization or quadrati� cation are investigated. We show that many important transformations are special instances of Möbius transformations, and analyze a Möbius connection between alternating and palindromic matrix polynomials. Finally, the use of Möbius transformations in solving polynomial inverse eigenproblems is illustrated. KW - Möbius transformation KW - matrix polynomial Y1 - 2014 UR - https://opus4.kobv.de/opus4-matheon/frontdoor/index/index/docId/1274 UR - https://nbn-resolving.org/urn:nbn:de:0296-matheon-12743 ER -