On the first and second order derivatives of the Perron vector
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.
scientific article; zbMATH DE number 3925016