Falseness of the finiteness property of the spectral subradius
International Journal of Applied Mathematics and Computer Science (2007)
- Volume: 17, Issue: 2, page 173-178
- ISSN: 1641-876X
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topCzornik, Adam, and Jurgas, Piotr. "Falseness of the finiteness property of the spectral subradius." International Journal of Applied Mathematics and Computer Science 17.2 (2007): 173-178. <http://eudml.org/doc/207829>.
@article{Czornik2007,
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.},
author = {Czornik, Adam, Jurgas, Piotr},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {finiteness property; spectral subradius},
language = {eng},
number = {2},
pages = {173-178},
title = {Falseness of the finiteness property of the spectral subradius},
url = {http://eudml.org/doc/207829},
volume = {17},
year = {2007},
}
TY - JOUR
AU - Czornik, Adam
AU - Jurgas, Piotr
TI - Falseness of the finiteness property of the spectral subradius
JO - International Journal of Applied Mathematics and Computer Science
PY - 2007
VL - 17
IS - 2
SP - 173
EP - 178
AB - 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.
LA - eng
KW - finiteness property; spectral subradius
UR - http://eudml.org/doc/207829
ER -
References
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