Products of tensors
| dc.contributor.author | Mabuza, Angel | |
| dc.contributor.supervisor | Hardy, Yorick | |
| dc.date.accessioned | 2025-11-18T11:20:38Z | |
| dc.date.issued | 2024-04 | |
| dc.description | A dissertation submitted in fulfilment of the requirements for the degree of Master of Science, to the Faculty of Science, School of Mathematics, University of the Witwatersrand, Johannesburg, 2025 | |
| dc.description.abstract | This dissertation surveys the products of tensors, their respective multilinear structures and their properties. Matrix products arise naturally from the composition of linear operations. In like manner, products of tensors derive from composing multilinear functions. However, there are many ways to compose multilinear functions, hence many forms of the product. We will gain further insight of linear operations and introduce the tensor-matrix multiplication (the simplest form of the compositional product). We will consider different types of products building up to the study of the general tensor-tensor multiplication defined in [Lin. Alg. Appl. 439, 2350–2366 (2013)]. Finally, we conclude with an investigation of some n-ary products of tensors. | |
| dc.description.sponsorship | GCRA | |
| dc.description.submitter | MM2024 | |
| dc.faculty | Faculty of Science | |
| dc.identifier | 0000-0002-1923-7775 | |
| dc.identifier.citation | Mabuza, Angel. (2024). Products of tensors. [Master's dissertation, University of the Witwatersrand, Johannesburg]. WIReDSpace. https://hdl.handle.net/10539/47683 | |
| dc.identifier.uri | https://hdl.handle.net/10539/47683 | |
| dc.language.iso | en | |
| dc.publisher | University of the Witwatersrand, Johannesburg | |
| dc.rights | ©2024 University of the Witwatersrand, Johannesburg. All rights reserved. The copyright in this work vests in the University of the Witwatersrand, Johannesburg. No part of this work may be reproduced or transmitted in any form or by any means, without the prior written permission of University of the Witwatersrand, Johannesburg. | |
| dc.rights.holder | University of the Witwatersrand, Johannesburg | |
| dc.school | School of Mathematics | |
| dc.subject | Tensor product | |
| dc.subject | T-product | |
| dc.subject | Einstein product | |
| dc.subject | Higher order singular value decomposition | |
| dc.subject | UCTD | |
| dc.subject.primarysdg | SDG-4: Quality education | |
| dc.subject.secondarysdg | SDG-9: Industry, innovation and infrastructure | |
| dc.title | Products of tensors | |
| dc.type | Dissertation |