Spectral Properties of a Sequence of Matrices Connected to Each Other via Schur Complement and Arising in a Compartmental Model

Authors

Evan Haskell, Nova Southeastern UniversityFollow
Vehbi Emrah Paksoy, Nova Southeastern UniversityFollow

Document Type

Article

Publication Date

1-2017

Publication Title

Special Matrices

Keywords

Schur complement, Routh-Hurwitz criterion, Elementary symmetric polynomials, Linear compartmental model, Latency phase

ISSN

2300-7451

Volume

5

Issue/No.

1

First Page

242

Last Page

250

Abstract

We consider a sequence of real matrices An which is characterized by the rule that A_n−1 is the Schur complement in A_n of the (1,1) entry of A_n, 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 A_n. In particular,we show that An has a unique positive eigenvalue λ_n and {λ_n} is a decreasing convergent sequence. We also study the stability of A_n for small n using the Routh-Hurwitz criterion.

Comments

©2017 Evan Haskell and Vehbi E. Paksoy, published by De Gruyter Open. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 License.

NSUWorks Citation

Haskell, Evan and Paksoy, Vehbi Emrah, "Spectral Properties of a Sequence of Matrices Connected to Each Other via Schur Complement and Arising in a Compartmental Model" (2017). Mathematics Faculty Articles. 206.
https://nsuworks.nova.edu/math_facarticles/206

DOI

10.1515/spma-2017-0017