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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-am42-1-3,
author = {Qassem M. Al-Hassan and Mowaffaq Hajja},
title = {A simple derivation of the eigenvalues of a tridiagonal matrix arising in biogeography},
journal = {Applicationes Mathematicae},
volume = {42},
year = {2015},
pages = {23-27},
zbl = {1329.15027},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am42-1-3}
}
Qassem M. Al-Hassan; Mowaffaq Hajja. A simple derivation of the eigenvalues of a tridiagonal matrix arising in biogeography. Applicationes Mathematicae, Tome 42 (2015) pp. 23-27. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am42-1-3/