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2-18.20

Cartesian coordinates of tensor

URNurn:iso:std:iso:80000:-2:ed-2:en:item:2-18.20

https://metanorma.github.io/isq-smart/math/part-2-18/t2-18.20
urn:iso:std:iso:80000:-2:ed-2:en:item:2-18.20

ISQ Identifiers

ISO

urn:iso:std:iso:80000:-2:ed-2:en:item:2-18.20

IEC

urn:iec:std:iec:80000-2:2019:::item:2-18.20

Designations

ENCartesian coordinates of tensor

FRcoordonnées cartésiennes d'un tenseur

Symbol

T_{x x}, T_{x y}, \dots, T_{z z}

T_{11}, T_{12}, \dots, T_{33}

Notation systems

AsciiMath

T_(x x), T_(xy), ..., T_(zz)

AsciiMath

T_(11), T_(12), ..., T_(33)

LaTeX

T_{x x} , T_{x y} , \ldots , T_{z z}

LaTeX

T_{11} , T_{12} , \ldots , T_{33}

Definition

Cartesian coordinates of tensor $T$ , + Cartesian components of tensor $T$

coordonnées cartésiennes du tenseur $T$ + composantes cartésiennes du tenseur $T$

Notes

The scalars $T_{x x}, T_{x y}, \dots, T_{z z}$ in the representation

$T = T_{x x} e_{x} e_{x} + T_{x y} e_{x} e_{y} + \dots + T_{z z} e_{z} e_{z}$

of the tensor $T$ by the base tensors

$e_{x} e_{x}, e_{x} e_{y}, \dots, e_{z} e_{z}$ .

$T_{x x} e_{x} e_{x}, T_{x y} e_{x} e_{y}, \dots, T_{z z} e_{z} e_{z}$ , are the component tensors.

If it is clear from the context which are the base vectors, the tensor can be written

$T = ([T_{x x}, T_{x y}, T_{x z} \$ ,[T_(yx), T_(yy), T_(yz)\],[T_(zx), T_(zy), T_(zz)\]) ].

Les scalaires $T_{x x}, T_{x y}, \dots, T_{z z}$ dans la représentation:

$T = T_{x x} e_{x} e_{x} + T_{x y} e_{x} e_{y} + \dots + T_{z z} e_{z} e_{z}$

du tenseur $T$ par les tenseurs de base

$e_{x} e_{x}, e_{x} e_{y}, \dots, e_{z} e_{z}$ .

$T_{x x} e_{x} e_{x}, T_{x y} e_{x} e_{y}, \dots, T_{z z} e_{z} e_{z}$ , sont les composantes du tenseur.

Si le contexte permet de savoir clairement quels sont les vecteurs de base, le tenseur peut être écrit:

$T = ([T_{x x}, T_{x y}, T_{x z} \$ ,[T_(yx), T_(yy), T_(yz)\],[T_(zx), T_(zy), T_(zz)\]) ].

Ontology
isq:MathConcept smart:TermEntry

Class Hierarchy

smart:Entity smart:TermEntryisq:MathConcept

A mathematical concept as defined in ISO/IEC 80000 Part 2.

Instance IRI

isq:t2-18.20

Properties

isq:MathConceptShape

Property	Value
rdf:type	isq:MathConcept smart:TermEntry
dcterms:identifier	2-18.20
skosxl:prefLabel	"Cartesian coordinates of tensor"@en
skosxl:altLabel	"T_(x x), T_(xy), ..., T_(zz)"@en"T_(11), T_(12), ..., T_(33)"@en
skos:definition	Cartesian coordinates of tensor stem:[sf(bb(ii(T)))], + Cartesian components of tensor stem:[sf(bb(ii(T)))]
skos:note	The scalars stem:[T_(x x), T_(xy), ..., T_(zz)] in the representation stem:[sf(bb(ii(T))) = T_(x x) e_x e_x + T_(xy) e_…
smart:hasBindingnessType	bindingness-type:normative
dcterms:isPartOf	isq:part-2-18

Related Entities

isq:MathConceptShape isq:part-2-18 smart:TermEntry