Higher derivatives and the inverse derivative of a tensor-valued function of a tensor

TL;DR

This paper introduces a formal framework for defining higher derivatives and inverse derivatives of tensor-valued functions of tensors, providing explicit formulas for their coefficients.

Contribution

It presents a novel approach to defining and computing derivatives of tensor functions with explicit closed-form coefficients.

Findings

Defined the n-th derivative of tensor-valued functions with explicit coefficients

Provided closed-form expressions for derivatives and inverse derivatives

Established a foundation for further tensor calculus applications

Abstract

The n-th derivative of a tensor valued function of a tensor is defined by a finite number of coefficients each with closed form expression.