Article
Spectral Properties of a Sequence of Matrices Connected to Each Other via Schur Complement and Arising in a Compartmental Model
Special Matrices
Document Type
Article
Publication Date
1-1-2017
Keywords
- Schur complement,
- Routh-Hurwitz criterion,
- Elementary symmetric polynomials,
- Linear compartmental model,
- Latency phase
Disciplines
Abstract
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.
DOI
10.1515/spma-2017-0017
Citation Information
Evan Haskell and Vehbi Emrah Paksoy. "Spectral Properties of a Sequence of Matrices Connected to Each Other via Schur Complement and Arising in a Compartmental Model" Special Matrices Vol. 5 Iss. 1 (2017) p. 242 - 250 ISSN: 2300-7451 Available at: http://works.bepress.com/evan-haskell/77/
©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.