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An alternative proof on higher order derivatives of a multilinear map
| dc.contributor.author | Carvalho, Sonia | |
| dc.date.accessioned | 2021-01-21T15:48:14Z | |
| dc.date.available | 2021-01-21T15:48:14Z | |
| dc.date.issued | 2020-07-02 | |
| dc.description.abstract | As a generalization of the formulas proved by Bhatia, Grover and Jain (Derivatives of tensor powers and their norms. Electron J Linear Algebra. 2013;26:604-619), in recent papers (The kth derivative of the immannant and the chi-symmetric tensor power of an operator. Electron J Linear Algebra. 2014;27:Article 18, On derivatives and norms of generalized matrix functions and respective symmetric powers. Electron J Linear Algebra. 2015;30:Article 22) Carvalho and Freitas obtained formulas for directional derivatives, of all orders, for generalized matrix functions and for every symmetric tensor power associated with a character xi of a subgroup G of the symmetric group S-m. Throughout our work, we used some well-known formulas for the derivatives of all orders of a multilinear map, since the maps that we studied are all multilinear. In this paper, we intend to present an alternative proof of these formulas, using the multilinearity argument. | pt_PT |
| dc.description.version | info:eu-repo/semantics/publishedVersion | pt_PT |
| dc.identifier.citation | CARVALHO, Sónia – An alternative proof on higher order derivatives of a multilinear map. Linear & Multilinear Algebra. ISSN 0308-1087. Vol. 68, N.º 7 (2020), pp. 1457-1464 | pt_PT |
| dc.identifier.doi | 10.1080/03081087.2018.1546816 | pt_PT |
| dc.identifier.eissn | 1563-5139 | |
| dc.identifier.issn | 0308-1087 | |
| dc.identifier.uri | http://hdl.handle.net/10400.21/12665 | |
| dc.language.iso | eng | pt_PT |
| dc.peerreviewed | yes | pt_PT |
| dc.publisher | Taylor & Francis | pt_PT |
| dc.relation.publisherversion | https://www.tandfonline.com/doi/pdf/10.1080/03081087.2018.1546816?needAccess=true | pt_PT |
| dc.subject | Multilinear map | pt_PT |
| dc.subject | Higher order derivatives | pt_PT |
| dc.subject | Multilinearity argument | pt_PT |
| dc.title | An alternative proof on higher order derivatives of a multilinear map | pt_PT |
| dc.type | journal article | |
| dspace.entity.type | Publication | |
| oaire.citation.endPage | 1464 | pt_PT |
| oaire.citation.issue | 7 | pt_PT |
| oaire.citation.startPage | 1457 | pt_PT |
| oaire.citation.title | Linear & Multilinear Algebra | pt_PT |
| oaire.citation.volume | 68 | pt_PT |
| person.familyName | Carvalho | |
| person.givenName | Sonia | |
| person.identifier.ciencia-id | E515-7135-3BA3 | |
| person.identifier.orcid | 0000-0002-8220-4079 | |
| rcaap.rights | closedAccess | pt_PT |
| rcaap.type | article | pt_PT |
| relation.isAuthorOfPublication | 3ec73205-17ff-4022-8ddb-e919c09825e5 | |
| relation.isAuthorOfPublication.latestForDiscovery | 3ec73205-17ff-4022-8ddb-e919c09825e5 |
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