@prefix psr: . @prefix skos: . @prefix dc: . @prefix xsd: . psr:-BPFXMP64-L skos:prefLabel "tensor calculus"@en, "calcul tensoriel"@fr ; a skos:Concept ; skos:narrower psr:-FLJ0HWTF-F . psr: a skos:ConceptScheme . psr:-FLJ0HWTF-F skos:broader psr:-BPFXMP64-L ; skos:inScheme psr: ; skos:narrower psr:-W8M3MG4C-K ; skos:definition """En mathématiques, le produit tensoriel est un moyen commode de coder les objets multilinéaires. Il est utilisé en algèbre, en géométrie différentielle, en géométrie riemannienne, en analyse fonctionnelle et en physique (mécanique des solides, relativité générale et mécanique quantique).
(Wikipedia, L'Encylopédie Libre, https://fr.wikipedia.org/wiki/Produit_tensoriel)"""@fr, """In mathematics, the tensor product

{\\\\displaystyle V\\\\otimes W}

of two vector spaces

V

and

W

(over the same field) is a vector space to which is associated a bilinear map

{\\\\displaystyle V\\ imes W\\ ightarrow V\\\\otimes W}

that maps a pair

{\\\\displaystyle (v,w),\\\\ v\\\\in V,w\\\\in W}

to an element of

{\\\\displaystyle V\\\\otimes W}

denoted

{\\\\displaystyle v\\\\otimes w.}

An element of the form

{\\\\displaystyle v\\\\otimes w}

is called the tensor product of

v

and

w

. An element of

{\\\\displaystyle V\\\\otimes W}

is a tensor, and the tensor product of two vectors is sometimes called an elementary tensor or a decomposable tensor. The elementary tensors span

{\\\\displaystyle V\\\\otimes W}

in the sense that every element of

{\\\\displaystyle V\\\\otimes W}

is a sum of elementary tensors. If bases are given for

V

and

W

, a basis of

{\\\\displaystyle V\\\\otimes W}

is formed by all tensor products of a basis element of

V

and a basis element of

W

.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Tensor_product)"""@en ; skos:exactMatch , ; skos:prefLabel "produit tensoriel"@fr, "tensor product"@en ; dc:modified "2024-10-18"^^xsd:date ; a skos:Concept . psr:-W8M3MG4C-K skos:prefLabel "Kronecker product"@en, "produit de Kronecker"@fr ; a skos:Concept ; skos:broader psr:-FLJ0HWTF-F .