A simple derivation of the eigenvalues of a tridiagonal matrix arising in biogeography

Qassem M. Al-Hassan, and Mowaffaq Hajja. "A simple derivation of the eigenvalues of a tridiagonal matrix arising in biogeography." Applicationes Mathematicae 42.1 (2015): 23-27. <http://eudml.org/doc/279887>.

@article{QassemM2015,
abstract = {In investigating a certain optimization problem in biogeography, Simon [IEEE Trans. Evolutionary Comput. 12 (2008), 702-713] encountered a certain specially structured tridiagonal matrix and made a conjecture regarding its eigenvalues. A few years later, the validity of the conjecture was established by Igelnik and Simon [Appl. Math. Comput. 218 (2011), 195-201]. In this paper, we give another proof of this conjecture that is much shorter, almost computation-free, and does not resort to the eigenvectors of the matrix.},
author = {Qassem M. Al-Hassan, Mowaffaq Hajja},
journal = {Applicationes Mathematicae},
keywords = {tridiagonal matrix; eigenvalue; eigenvector; biogeography},
language = {eng},
number = {1},
pages = {23-27},
title = {A simple derivation of the eigenvalues of a tridiagonal matrix arising in biogeography},
url = {http://eudml.org/doc/279887},
volume = {42},
year = {2015},
}

TY - JOUR
AU - Qassem M. Al-Hassan
AU - Mowaffaq Hajja
TI - A simple derivation of the eigenvalues of a tridiagonal matrix arising in biogeography
JO - Applicationes Mathematicae
PY - 2015
VL - 42
IS - 1
SP - 23
EP - 27
AB - In investigating a certain optimization problem in biogeography, Simon [IEEE Trans. Evolutionary Comput. 12 (2008), 702-713] encountered a certain specially structured tridiagonal matrix and made a conjecture regarding its eigenvalues. A few years later, the validity of the conjecture was established by Igelnik and Simon [Appl. Math. Comput. 218 (2011), 195-201]. In this paper, we give another proof of this conjecture that is much shorter, almost computation-free, and does not resort to the eigenvectors of the matrix.
LA - eng
KW - tridiagonal matrix; eigenvalue; eigenvector; biogeography
UR - http://eudml.org/doc/279887
ER -