A short note on the ratio between sign-real and sign-complex spectral radius of a real square matrix

Publikationstyp
Journal Article
Date Issued
2017-09-15
Sprache
English
Author(s)
Bünger, Florian  
Institut
Zuverlässiges Rechnen E-19  
TORE-URI
http://hdl.handle.net/11420/3852
Journal
Linear algebra and its applications  
Volume
529
Start Page
126
End Page
132
Citation
Linear Algebra and Its Applications (529): 126-132 (2017-09-15)
Publisher DOI
10.1016/j.laa.2017.04.022
Scopus ID
2-s2.0-85018274310
For a real (n×n)-matrix A the sign-real and the sign-complex spectral radius – invented by Rump – are respectively defined as ρR(A):=max⁡|λ|||Ax|=|λx|,λ∈R,x∈Rn{0,ρC(A):=max⁡|λ|||Ax|=|λx|,λ∈C,x∈Cn{0. For n≥2 we prove ρR(A)≥ζn ρC(A) where the constant ζn:=[formula omitted] is best possible.
Subjects
Eigenvalue inequalities
Sign-complex spectral radius
Sign-real spectral radius
Spectral radius