On Derivatives and Norms of Generalized Matrix Functions and Respective Symmetric Powers

Abstract

In recent papers, S. Carvalho and P. J. Freitas obtained formulas for directional derivatives, of all orders, of the immanant and of the m-th $\xi$-symmetric tensor power of an operator and a matrix, when $\xi$ is a character of the full symmetric group. The operator bound norm of these derivatives was also calculated. In this paper similar results are established for generalized matrix functions and for every symmetric tensor power.