2019/10/27 by Philip Saltenberger, Saltenberger, Philip
Computer Science · Mathematics · #11E39 #15A23 #15A63 #15B10 #15B57 #Advanced Algebra and Geometry #Advanced Topics in Algebra #FOS: Mathematics #Matrix Theory and Algorithms #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.1910.12307
openalex publication_date 2019/10/27 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28
In this work some results on the structure-preserving diagonalization of\nselfadjoint and skewadjoint matrices in indefinite inner product spaces are\npresented. In particular, necessary and sufficient conditions on the symplectic\ndiagonalizability of (skew)-Hamiltonian matrices and the perplectic\ndiagonalizability of per(skew)-Hermitian matrices are provided. Assuming the\nstructured matrix at hand is additionally normal, it is shown that any\nsymplectic or perplectic diagonalization can always be constructed to be\nunitary. As a consequence of this fact, the existence of a unitary,\nstructure-preserving diagonalization is equivalent to the existence of a\nspecially structured additive decomposition of such matrices. The implications\nof this decomposition are illustrated by several examples.\n