Open AccessOn the density of semisimple matrices in indefinite scalar product spaces
Author(s) -
Ralph John de la Cruz,
Philip Saltenberger
Publication year - 2021
Publication title -
the electronic journal of linear algebra
Language(s) - English
Resource type - Journals
eISSN - 1537-9582
pISSN - 1081-3810
DOI - 10.13001/ela.2021.5509
Subject(s) - mathematics , diagonalizable matrix , unitary state , scalar (mathematics) , product (mathematics) , cartesian product , complex matrix , pure mathematics , combinatorics , symmetric matrix , physics , eigenvalues and eigenvectors , chemistry , quantum mechanics , geometry , chromatography , political science , law
For an indefinite scalar product $[x,y]_B = x^HBy$ for $B= \pm B^H \in \mathbf{Gl}_n(\mathbb{C})$ on $\mathbb{C}^n \times \mathbb{C}^n$, it is shown that the set of diagonalizable matrices is dense in the set of all $B$-normal matrices. The analogous statement is also proven for the sets of $B$-selfadjoint, $B$-skewadjoint and $B$-unitary matrices.