On the density of semisimple matrices in indefinite scalar product spaces

Autor:	Ralph John de la Cruz, Philip Saltenberger
Rok vydání:	2021
Předmět:	Statement (computer science) Set (abstract data type) Pure mathematics Algebra and Number Theory Sesquilinear form Product (mathematics) Scalar (mathematics) Diagonalizable matrix Unitary matrix Normal matrix Mathematics
Zdroj:	The Electronic Journal of Linear Algebra. 37:387-401
ISSN:	1081-3810
DOI:	10.13001/ela.2021.5509
Popis:	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.
Databáze:	OpenAIRE
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