On the derivative of the Perron vector whose infinity norm is fixed
Emeric Deutsch, Michael Neumann · Linear and Multilinear Algebra · 1987
In the recent paper the authors studied the derivaties of the Perron vector at an n × n essentially nonnegative and irreducible matrix A when the Perron vector is subjected to the normalization that one of its components is held a fixed constant in a neighbourhood of A or that the pth norm of the of the eigenvector is held a fixed constant in such a neighborhood. The Perron vector subject to the normalization that its infinity norm is held a fixed constant in a neighborhood of A does not necessarily imply that it is differentiable at A. In this paper we give formulas for the first derivative of this Perron vector where it is differentiable. Our formulas also accommodate left and right derivatives of the eigenvector.