Rank and symmetries of signature tensors
Abstract
The signature of a path is a sequence of tensors which allows to uniquely reconstruct the path. In this paper we propose a systematic study of basic properties of signature tensors, starting from their rank, symmetries and conciseness. We prove a sharp upper bound on the rank of signature tensors of piecewise linear paths. We show that there are no skew-symmetric signature tensors of order three or more, and we also prove that specific instances of partial symmetry can only happen for tensors of order three. Finally, we give a simple geometric characterization of paths whose signature tensors are not concise.
- Publication:
-
arXiv e-prints
- Pub Date:
- July 2024
- DOI:
- 10.48550/arXiv.2407.20405
- arXiv:
- arXiv:2407.20405
- Bibcode:
- 2024arXiv240720405G
- Keywords:
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- Mathematics - Algebraic Geometry;
- 14N07;
- 15A69;
- 15A72;
- 60L10