On the derivatives of a subclass of isotropic tensor functions of a nonsymmetric tensor

Abstract

This paper studies a subclass of isotropic tensor-valued functions of a nonsymmetric tensor, which satisfy the commutative condition, and their derivatives. This subclass of tensor functions includes tensor power series, exponential tensor function, etc., and is more general than those investigated before. In the case of three distinct eigenvalues, the derivatives of these tensor functions are constructed by solving a tensor equation, which is acquired by differentiating the commutative condition. By taking limits, the results are extended to the cases of repeated eigenvalues.