<abstract xml:lang="en" xmlns="http://www.w3.org/1999/xhtml"><p>We prove that there exist infinitely may values of the real parameter α for which the exact value of the spectral subradius of the set of two matrices (one matrix with ones above and on the diagonal and zeros elsewhere, and one matrix with α below and on the diagonal and zeros elsewhere, both matrices having two rows and two columns) cannot be calculated in a finite number of steps. Our proof uses only elementary facts from the theory of formal languages and from linear algebra, but it is not constructive because we do not show any explicit value of α that has described property. The problem of finding such values is still open.</p></abstract>

We prove that there exist infinitely may values of the real parameter α for which the exact value of the spectral subradius of the set of two matrices (one matrix with ones above and on the diagonal and zeros elsewhere, and one matrix with α below and on the diagonal and zeros elsewhere, both matrices having two rows and two columns) cannot be calculated in a finite number of steps. Our proof uses only elementary facts from the theory of formal languages and from linear algebra, but it is not constructive because we do not show any explicit value of α that has described property. The problem of finding such values is still open.

Falseness of the Finiteness Property of the Spectral Subradius

Department of Automatic Control, Silesian University of Technology, ul. Akademicka 17, 44-101 Gliwice, Poland

Polish-Japanese Institute of Information Technology, ul. Aleja Legionów 2, 41-902 Bytom

International Journal of Applied Mathematics and Computer Science

{"article-title":"Falseness of the Finiteness Property of the Spectral Subradius"}

We prove that there exist infinitely may values of the real parameter α for which the exact value of the spectral subradius of the set of two matrices (one...

Falseness of the Finiteness Property of the Spectral Subradius

Publié en ligne: 17 juil. 2007

Pages: 173 - 178

DOI: https://doi.org/10.2478/v10006-007-0016-1

Mots clés
finiteness property, spectral subradius

This content is open access.

Falseness of the Finiteness Property of the Spectral Subradius

Publié en ligne: 17 juil. 2007

Pages: 173 - 178

DOI: https://doi.org/10.2478/v10006-007-0016-1

Mots clésfiniteness property, spectral subradius

This content is open access.

Mots clés
finiteness property, spectral subradius