Eigenvalue problem for some special class of anti-triangular matrices
Rings and Algebras
2014-03-27 v1 Probability
Abstract
We study the eigenvalue problem for some special class of anti-triangular matrices. Though the eigenvalue problem is quite classical, as far as we know, almost nothing is known about properties of eigenvalues for anti-triangular matrices. In this paper, we show that there is a nice class of anti-triangular matrices whose eigenvalues are given explicitly by their elements. Moreover, this class contains several interesting subclasses which we characterize in terms of probability measures. We also discuss the application of our main theorem to the study of interacting particle systems, which are stochastic processes studied in extensive literature.
Cite
@article{arxiv.1403.6797,
title = {Eigenvalue problem for some special class of anti-triangular matrices},
author = {Hiroyuki Ochiai and Makiko Sasada and Tomoyuki Shirai and Takashi Tsuboi},
journal= {arXiv preprint arXiv:1403.6797},
year = {2014}
}