On the first and second order derivatives of the Perron vector
type: Item
instance of: scholarly article
title: On the first and second order derivatives of the Perron vector
zbMATH Open document ID: 0578.15018
DOI: 10.1016/0024-3795(85)90235-6
author: Emeric Deutsch
author: M. Neumann
published in: Linear Algebra and its Applications
publication date: 1985-01-01T00:00:00Z
review text: For an essentially nonnegative irreducible matrix A the first and second derivatives of the Perron vector as a function of the matrix entries are studied. Explicit formulas are given for certain normalizations of the Perron vector and the case that only the elements in the first row are perturbed and are either linear functions of one parameter or variables independent of each other. Conditions are given under which the Perron vector is a convex function. They involve the group generalized inverse \(Q^{\#}\) of \(Q=sI-A\), where s is the Perron root of A.
Mathematics Subject Classification ID: 15B48
Mathematics Subject Classification ID: 15A42
Mathematics Subject Classification ID: 15A09
zbMATH DE Number: 3925016
zbMATH Keywords: convexity
zbMATH Keywords: group generalized inverse
zbMATH Keywords: second derivative
zbMATH Keywords: Perron
zbMATH Keywords: root
zbMATH Keywords: nonnegative irreducible matrix
zbMATH Keywords: Perron vector
reviewed by: Ludwig Elsner
MaRDI profile type: Publication
full work available at URL: 0024-3795(85)90235-6
OpenAlex ID: W2068042605
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description: scientific article; zbMATH DE number 3925016