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# On sign-real spectral radii and sign-real expansive matrices

Publikationstyp

Journal Article

Publikationsdatum

2024-01-01

Sprache

English

Enthalten in

Volume

680

Start Page

293

End Page

324

Citation

Linear Algebra and Its Applications 680: 293-324 (2024-01-01)

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.