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

Evan Haskell; Vehbi Emrah Paksoy

doi:10.1515/spma-2017-0017

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

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	American English
Pages (from-to)	242-249
Number of pages	8
Journal	Special Matrices
Volume	5
Issue number	1
DOIs	https://doi.org/10.1515/spma-2017-0017
State	Published - Oct 26 2017

Bibliographical note

Publisher Copyright:
© 2017 Evan Haskell and Vehbi E. Paksoy, published by De Gruyter Open.

ASJC Scopus Subject Areas

Algebra and Number Theory
Geometry and Topology

Keywords

Schur complement
Routh-Hurwitz criterion
Elementary symmetric polynomials
Linear compartmental model
Latency phase
elementary symmetric polynomials
linear compartmental model
latency phase

Disciplines

Mathematics
Physical Sciences and Mathematics

Access to Document

10.1515/spma-2017-0017License: CC BY

Spectral Properties of a Sequence of Matrices Connected to Each OFinal published version, 412 KBLicense: CC BY
Spectral Properties of a Sequence of Matrices Connected to Each OFinal published version, 412 KBLicense: CC BY

Cite this

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

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.",

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author = "Evan Haskell and Paksoy, \{Vehbi Emrah\}",

note = "Publisher Copyright: {\textcopyright} 2017 Evan Haskell and Vehbi E. Paksoy, published by De Gruyter Open.",

year = "2017",

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doi = "10.1515/spma-2017-0017",

language = "American English",

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T1 - Spectral Properties of a Sequence of Matrices Connected to Each Other via Schur Complement and Arising in a Compartmental Model

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AU - Paksoy, Vehbi Emrah

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Y1 - 2017/10/26

N2 - 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.

AB - 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.

KW - Schur complement

KW - Routh-Hurwitz criterion

KW - Elementary symmetric polynomials

KW - Linear compartmental model

KW - Latency phase

KW - elementary symmetric polynomials

KW - linear compartmental model

KW - latency phase

UR - https://nsuworks.nova.edu/math_facarticles/206

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U2 - 10.1515/spma-2017-0017

DO - 10.1515/spma-2017-0017

M3 - Article

SN - 2300-7451

VL - 5

SP - 242

EP - 249

JO - Special Matrices

JF - Special Matrices

IS - 1

ER -

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

Abstract

Bibliographical note

ASJC Scopus Subject Areas

Keywords

Disciplines

Access to Document

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