{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,7]],"date-time":"2025-11-07T20:18:17Z","timestamp":1762546697659,"version":"build-2065373602"},"publisher-location":"Cham","reference-count":4,"publisher":"Springer Nature Switzerland","isbn-type":[{"value":"9783031972386","type":"print"},{"value":"9783031972393","type":"electronic"}],"license":[{"start":{"date-parts":[[2025,11,8]],"date-time":"2025-11-08T00:00:00Z","timestamp":1762560000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2025,11,8]],"date-time":"2025-11-08T00:00:00Z","timestamp":1762560000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2026]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>\n                    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\u2014the 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\n                    <jats:italic>tensor algebra<\/jats:italic>\n                    .\n                  <\/jats:p>","DOI":"10.1007\/978-3-031-97239-3_2","type":"book-chapter","created":{"date-parts":[[2025,11,7]],"date-time":"2025-11-07T20:14:20Z","timestamp":1762546460000},"page":"65-83","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["An Introduction to Tensors for Path Signatures"],"prefix":"10.1007","author":[{"given":"Jack","family":"Beda","sequence":"first","affiliation":[]},{"given":"Gon\u00e7alo","family":"dos Reis","sequence":"additional","affiliation":[]},{"given":"Nikolas","family":"Tapia","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,11,8]]},"reference":[{"key":"2_CR1","doi-asserted-by":"crossref","unstructured":"J. Diestel, J.H. Fourie, J. Swart, The Metric Theory of Tensor Products (American Mathematical Society, Providence, RI, 2008). Grothendieck\u2019s r\u00e9sum\u00e9 revisited","DOI":"10.1090\/mbk\/052"},{"key":"2_CR2","doi-asserted-by":"crossref","unstructured":"W. Hackbusch, Tensor spaces and numerical tensor calculus, in Springer Series in Computational Mathematics, vol. 56, 2nd edn. (Springer, Cham, 2019)","DOI":"10.1007\/978-3-030-35554-8"},{"key":"2_CR3","unstructured":"S. Rabanser, O. Shchur, S. G\u00fcnnemann, Introduction to tensor decompositions and their applications in machine learning. arXiv:1711.10781 (2017)"},{"key":"2_CR4","unstructured":"M. Reed, B. Simon, Methods of Modern Mathematical Physics I, 2nd edn. (Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York, 1980). Functional analysis"}],"container-title":["Springer Finance","Signature Methods in Finance"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-031-97239-3_2","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,11,7]],"date-time":"2025-11-07T20:14:21Z","timestamp":1762546461000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-031-97239-3_2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,11,8]]},"ISBN":["9783031972386","9783031972393"],"references-count":4,"URL":"https:\/\/doi.org\/10.1007\/978-3-031-97239-3_2","relation":{},"ISSN":["1616-0533","2195-0687"],"issn-type":[{"value":"1616-0533","type":"print"},{"value":"2195-0687","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,11,8]]},"assertion":[{"value":"8 November 2025","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}}]}}