Simple forms for perplectic and symplectic normal matrices

Autor:	Ralph John de la Cruz, Philip Saltenberger
Rok vydání:	2021
Předmět:	Numerical Analysis Algebra and Number Theory Dense set Nowhere dense set Diagonalizable matrix Normal matrix Combinatorics Matrix (mathematics) Adjugate matrix Simple (abstract algebra) Discrete Mathematics and Combinatorics Geometry and Topology Mathematics Symplectic geometry
Zdroj:	Linear Algebra and its Applications. 620:201-227
ISSN:	0024-3795
DOI:	10.1016/j.laa.2021.03.003
Popis:	Let B = J 2 n or B = R n for the matrices given by J 2 n = [ I n − I n ] ∈ M 2 n ( C ) or R n = [ 1 ⋰ 1 ] ∈ M n ( C ) . A matrix A is called B-normal if A A ⋆ = A ⋆ A holds for A and its adjoint matrix A ⋆ : = B − 1 A H B . In addition, a matrix Q is called B-unitary, if Q H B Q = B . We develop sparse simple forms for nondefective (i.e. diagonalizable) J 2 n / R n -normal matrices under J 2 n / R n -unitary similarity transformations. For both cases we show that these forms exist for an open and dense subset of J 2 n / R n -normal matrices. This implies that these forms can be seen as topologically ‘generic’ since they exist for all J 2 n / R n -normal matrices except a nowhere dense subset.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::fd2ad665d6bd623805a107b8f56fa30b https://doi.org/10.1016/j.laa.2021.03.003 Zobrazit plný text záznamu Full Text from ScienceDirect