Solving Linear Tensor Equations

We develop a systematic way to solve linear equations involving tensors of arbitrary rank. We start off with the case of a rank 3 tensor, which appears in many applications, and after finding the condition for a unique solution we derive this solution. Subsequently, we generalize our result to tensors of arbitrary rank. Finally, we consider a generalized version of the former case of rank 3 tensors and extend the result when the tensor traces are also included.