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Introduction ` a l’alg` ebre tensorielle Patrick Gros To cite this version: Patrick Gros. Introduction ` a l’alg` ebre tensorielle. [Rapport de recherche] RT-0238, INRIA. 2000, pp.17. <inria-00069934> HAL Id: inria-00069934 https://hal.inria.fr/inria-00069934 Submitted on 19 May 2006 HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destin´ ee au d´ epˆ ot et ` a la diffusion de documents scientifiques de niveau recherche, publi´ es ou non, ´ emanant des ´ etablissements d’enseignement et de recherche fran¸cais ou ´ etrangers, des laboratoires publics ou priv´ es.

Introduction a l’alg ebre tensorielle · 2016. 12. 27. · destin ee au d ep^ot et a la di usion de documents scienti ques de niveau recherche, publi es ou non, emanant des etablissements

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  • Introduction à l’algèbre tensorielle

    Patrick Gros

    To cite this version:

    Patrick Gros. Introduction à l’algèbre tensorielle. [Rapport de recherche] RT-0238, INRIA.2000, pp.17.

    HAL Id: inria-00069934

    https://hal.inria.fr/inria-00069934

    Submitted on 19 May 2006

    HAL is a multi-disciplinary open accessarchive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished or not. The documents may come fromteaching and research institutions in France orabroad, or from public or private research centers.

    L’archive ouverte pluridisciplinaire HAL, estdestinée au dépôt et à la diffusion de documentsscientifiques de niveau recherche, publiés ou non,émanant des établissements d’enseignement et derecherche français ou étrangers, des laboratoirespublics ou privés.

    https://hal.archives-ouvertes.frhttps://hal.inria.fr/inria-00069934

  • ISS

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    INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE

    Introduction à l’algèbre tensorielle

    Patrick�������

    IRISA – CNRS

    N˚0238

    Février 2000

    THÈME 3

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  • Unité de recherche INRIA Lorraine, Technopôle de Nancy-Brabois, Campus scientifique,615 rue du Jardin Botanique, BP 101, 54600 VILLERS LÈS NANCY

    Unité de recherche INRIA Rennes, Irisa, Campus universitaire de Beaulieu, 35042 RENNES CedexUnité de recherche INRIA Rhône-Alpes, 655, avenue de l’Europe, 38330 MONTBONNOT ST MARTIN

    Unité de recherche INRIA Rocquencourt, Domaine de Voluceau, Rocquencourt, BP 105, 78153 LE CHESNAY CedexUnité de recherche INRIA Sophia-Antipolis, 2004 route des Lucioles, BP 93, 06902 SOPHIA-ANTIPOLIS Cedex

    ÉditeurINRIA, Domaine de Voluceau, Rocquencourt, BP 105, 78153 LE CHESNAY Cedex (France)��������� ����

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    ISSN 0249-0803

    1 Approche intuitive1.1 Introduction des tenseurs1.2 Covariance et contravariance1.3 Invariants d'un tenseur

    2 Dualité2.1 Espaces dual et bidual2.2 Changement de base

    3 Approche mathématique3.1 Définition des tenseurs3.2 Produit tensoriel3.3 Décomposition d'un tenseur sur une base3.3.1 Recherche d'une base3.3.2 Exemples3.3.3 Composantes d'un produit tensoriel

    3.4 Changements de base3.5 Contraction et invariants3.5.1 Contraction d'un tenseur3.5.2 Invariants

    3.6 Tenseurs dans un espace euclidien