On the quasimonotonicity of a square linear operator with respect to a nonnegative cone
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Authors
Beaver, Philip
Subjects
Essentially nonnegative matrices
Vector Lyapunov functions
Nonnegative cones
Vector Lyapunov functions
Nonnegative cones
Advisors
Canright, David
Date of Issue
1998-06
Date
Publisher
Monterey, California. Naval Postgraduate School
Language
en_US
Abstract
The question of when a square, linear operator is quasimonotone nondecreasing with respect to a nonnegative cone was posed for the application of vector Lyapunov functions in 1974. Necessary conditions were given in 1980, which were based on the spectrum and the first eigenvector. This dissertation gives necessary and sufficient conditions for the case of the real spectrum when the first eigenvector is in the nonnegative orthant, and when the first eigenvector is in the boundary of the nonnegative orthant, it gives conditions based on the reducibility of the matrix. For the complex spectrum, in the presence of a positive first eigenvector the problem is shown to be equivalent to the irreducible nonnegative inverse eigenvalue problem
Type
Thesis
Description
Series/Report No
Department
Applied Mathematics
Organization
Identifiers
NPS Report Number
Sponsors
Funder
Format
x, 96 p.;28 cm.
Citation
Distribution Statement
Approved for public release; distribution is unlimited.