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Solving Linear Tensor Equations

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arxiv 2109.08893 v1 pith:S6O46XUP submitted 2021-09-18 math-ph math.DGmath.MP

Damianos Iosifidis This is my paper · ORCID
classification math-phmath.DGmath.MP
keywords ranktensortensorsarbitrarycaseequationslinearresult
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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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