The distribution of eigenvalues of doubly cyclic Z+-matrices

Charles R. Johnson; Zachary Price; Ilya M. Spitkovsky

doi:10.1016/j.laa.2013.09.021

The distribution of eigenvalues of doubly cyclic Z⁺-matrices

Charles R. Johnson, Zachary Price, Ilya M. Spitkovsky

Mathematics

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

Abstract

It is shown that every matrix in a large class of n-by-n doubly cyclic Z⁺ matrices with negative determinant has exactly one eigenvalue in the closed left half-plane. This generalizes a result for n=4 used in a recent analysis of cancer cell dynamics. A further conjecture is made based on computational evidence. All work relates to the inertia of certain doubly cyclic circulants.

Original language	English (US)
Pages (from-to)	3576-3580
Number of pages	5
Journal	Linear Algebra and Its Applications
Volume	439
Issue number	11
DOIs	https://doi.org/10.1016/j.laa.2013.09.021
State	Published - Dec 1 2013

Keywords

Doubly-cyclic Z matrices
Eigenvalue location

ASJC Scopus subject areas

Algebra and Number Theory
Numerical Analysis
Geometry and Topology
Discrete Mathematics and Combinatorics

Access to Document

10.1016/j.laa.2013.09.021

Cite this

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title = "The distribution of eigenvalues of doubly cyclic Z+-matrices",

abstract = "It is shown that every matrix in a large class of n-by-n doubly cyclic Z+ matrices with negative determinant has exactly one eigenvalue in the closed left half-plane. This generalizes a result for n=4 used in a recent analysis of cancer cell dynamics. A further conjecture is made based on computational evidence. All work relates to the inertia of certain doubly cyclic circulants.",

keywords = "Doubly-cyclic Z matrices, Eigenvalue location",

author = "Johnson, {Charles R.} and Zachary Price and Spitkovsky, {Ilya M.}",

note = "Funding Information: This research was supported in part by the NSF CSUMS grant DMS-0703532 . ",

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AU - Price, Zachary

AU - Spitkovsky, Ilya M.

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PY - 2013/12/1

Y1 - 2013/12/1

N2 - It is shown that every matrix in a large class of n-by-n doubly cyclic Z+ matrices with negative determinant has exactly one eigenvalue in the closed left half-plane. This generalizes a result for n=4 used in a recent analysis of cancer cell dynamics. A further conjecture is made based on computational evidence. All work relates to the inertia of certain doubly cyclic circulants.

AB - It is shown that every matrix in a large class of n-by-n doubly cyclic Z+ matrices with negative determinant has exactly one eigenvalue in the closed left half-plane. This generalizes a result for n=4 used in a recent analysis of cancer cell dynamics. A further conjecture is made based on computational evidence. All work relates to the inertia of certain doubly cyclic circulants.

KW - Doubly-cyclic Z matrices

KW - Eigenvalue location

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