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An Introduction to Tensors for Path Signatures

In: Signature Methods in Finance

Author

Listed:
  • Jack Beda

    (University of Edinburgh)

  • Gonçalo dos Reis

    (University of Edinburgh
    Center for Mathematics and Applications (NOVA Math))

  • Nikolas Tapia

    (Weierstrass Institute
    Humboldt University Berlin)

Abstract

We present a fit-for-purpose introduction to tensors and their operations. It is envisaged to help the reader become acquainted with its underpinning concepts for the study of path signatures. The text includes exercises, solutions and many intuitive explanations. The material discusses direct sums and tensor products as two possible operations that make the Cartesian product of vectors spaces a vector space. The difference lies in linear vs. multilinear structures—the latter being the suitable one to deal with path signatures. The presentation is offered to understand tensors in a sense deeper than just a multidimensional array. The text concludes with the prime example of an algebra in relation to path signatures: the tensor algebra.

Suggested Citation

  • Jack Beda & Gonçalo dos Reis & Nikolas Tapia, 2026. "An Introduction to Tensors for Path Signatures," Springer Finance, in: Christian Bayer & Goncalo dos Reis & Blanka Horvath & Harald Oberhauser (ed.), Signature Methods in Finance, pages 65-83, Springer.
    • Handle: RePEc:spr:sprfcp:978-3-031-97239-3_2
    DOI: 10.1007/978-3-031-97239-3_2
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