We consider a sequence of real matrices An which is characterized by the rule that An−1 is the Schur complement in An of the (1,1) entry of An, namely −en, where en is a positive real number. This sequence is closely related to linear compartmental ordinary differential equations. We study the spectrum of An. In particular,we show that An has a unique positive eigenvalue λn and {λn} is a decreasing convergent sequence. We also study the stability of An for small n using the Routh-Hurwitz criterion.
@article{bwmeta1.element.doi-10_1515_spma-2017-0017,
author = {Evan C. Haskell and Vehbi E. Paksoy},
title = {Spectral properties of a sequence of matrices connected to each other via Schur complement and arising in a compartmental model},
journal = {Special Matrices},
volume = {5},
year = {2017},
pages = {242-249},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_spma-2017-0017}
}
Evan C. Haskell; Vehbi E. Paksoy. Spectral properties of a sequence of matrices connected to each other via Schur complement and arising in a compartmental model. Special Matrices, Tome 5 (2017) pp. 242-249. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_spma-2017-0017/