Rank-one corrections of nonnegative matrices, with an application to matrix population models
type: Item
instance of: scholarly article
zbMATH Open document ID: 1305.15076
DOI: 10.1137/130935537
author: Vladimir Yu. Protasov
author: Dmitrii O. Logofet
published in: SIAM Journal on Matrix Analysis and Applications
publication date: 2014-10-15T00:00:00Z
Mathematics Subject Classification ID: 15B48
Mathematics Subject Classification ID: 15B51
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 15A18
zbMATH DE Number: 6356195
zbMATH Keywords: nonnegative matrix
zbMATH Keywords: spectral radius
zbMATH Keywords: second largest eigenvalue
zbMATH Keywords: rank-one correction
zbMATH Keywords: matrix population model
zbMATH Keywords: projection matrix
zbMATH Keywords: indicator function
zbMATH Keywords: recruiting stage
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1137/130935537
OpenAlex ID: W2070239140
Recommended article: Perturbation of Matrices and Nonnegative Rank with a View toward Statistical Models
Recommended article: Nonnegative matrices as a tool to model population dynamics: Classical models and contemporary expansions
Recommended article: Q3624245
Recommended article: A contribution of sparse matrices tools to matrix population model analysis
Recommended article: Fixed rank solutions of the matrix equation with statistical applications
Recommended article: Probability matrices, non-negative rank, and parameterization of mixture models
Recommended article: Two Novel proofs of Spectral Monotonicity of Perturbed Essentially Nonnegative Matrices with Applications in Population Dynamics
Recommended article: Matrix rank and inertia formulas in the analysis of general linear models
Recommended article: SOME FURTHER NOTES ON THE USE OF MATRICES IN POPULATION MATHEMATICS
Recommended article: Stability indicatrices of nonnegative matrices and some of their applications in problems of biology and epidemiology
title: Rank-one corrections of nonnegative matrices, with an application to matrix population models
review text: The authors study the location of the second largest eigenvalue of a nonnegative matrix and what occurs with such a number under rank-one corrections. The main result proves that if a matrix \(B\) is a rank-one correction of a matrix \(A\) (both nonnegative), then \(B\) has at most one real eigenvalue (which is simple) greater than the leading eigenvalue of \(A\). It is shown that the analogue of such result is not true for eigenvalue modulus or for the eigenvalue real parts. Such results are applicable to matrix population models where the location of the second largest positive eigenvalue plays a crucial role.
reviewed by: Carlos F. Lardizabal
description: scientific article; zbMATH DE number 6356195