Solving Linear Tensor Equations

2021/09/18 by Damianos Iosifidis, Iosifidis, Damianos
Mathematics · Physics and Astronomy · #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.DG #math.MP

paper · pdf · doi:10.48550/arxiv.2109.08893

7 pages, no figures

arxiv created 2021/09/18 · arxiv updated 2021/09/21

Abstract

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.

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