Options
On sign-real spectral radii and sign-real expansive matrices
Publikationstyp
Journal Article
Date Issued
2024-01-01
Sprache
English
Author(s)
Volume
680
Start Page
293
End Page
324
Citation
Linear Algebra and Its Applications 680: 293-324 (2024)
Publisher DOI
Scopus ID
Publisher
Elsevier
Let Mn be the space of real matrices of order n. The sign-real spectral radius ξ:Mn→R+, introduced in a 1997 paper by S.M. Rump, intervenes for instance in the problem of estimating the componentwise distance to singularity. The function ξ has also a bearing in the analysis of generalized absolute value equations and linear complementarity problems. Although ξ is not a norm, it is at least absolutely homogeneous and continuous. Furthermore, ξ is invariant under transposition, permutation similarity, and a few other linear isomorphisms on Mn. A matrix A∈Mn is called sign-real expansive if ξ(A)≥1. Let Ωn be the set of such matrices. The purpose of this work is to discover new properties of the function ξ and to explore in detail the structure of the set Ωn.
Subjects
Absolute value equations and inequalities
Sign-real expansive matrix
Sign-real spectral radius
DDC Class
510: Mathematics