tensor

See also:Tensorandtensör

English

Etymology

Borrowed fromNew Latintensor(“that which stretches”),equivalent totense+‎-or.Anatomical sense from 1704. Introduced in the 1840s byWilliam Rowan Hamiltonas an algebraic quantity unrelated to the modern notion of tensor. The contemporary mathematical meaning was introduced (asGermanTensor) by Woldemar Voigt (1898)and adopted in English from 1915 (in the context ofgeneral relativity), obscuring the earlier Hamiltonian sense. The mathematical object is so named because an early application of tensors was the study of materials stretching undertension.(See, for example,Cauchy stress tensoron Wikipedia.Wikipedia)

Pronunciation

• (Received Pronunciation)IPA^(key):/ˈtɛn.sə/,/ˈtɛn.sɔː/

• Audio(Southern England):

  (file)

• (General American)IPA^(key):/ˈtɛn.sɚ/,/ˈtɛn.sɔɹ/
• Rhymes:-ɛnsə(ɹ)

Noun

tensor(pluraltensorsor(muscle)tensores)

1. (anatomy)Amusclethattightensorstretchesa part, or renders ittense.[from 17th c.]

   Hyponyms:tensor fasciae latae,tensor tympani,tensor veli palatini

2. (mathematics,linear algebra,physics)Amathematicalobject that describeslinearrelations onscalars,vectors,matricesand otheralgebraicobjects, and is represented as amultidimensional array.[from 18th c.]

   Hypernym:function

   Hyponyms:duotensor,eigentensor,Faraday tensor,hypertensor,metric tensor,pseudotensor,subtensor,supertensor,vector,Weyl tensor,zero tensor

   • 1963,Richard Feynman,“Chapter 31, Tensors”,inThe Feynman Lectures on Physics,volume II:

     Thetensor$\alpha _{ij}$should really be called a “tensorof second rank,” because it has two indexes. A vector—withoneindex—is atensorof the first rank, and a scalar—with no index—is atensorof zero rank.

3. (mathematics,obsolete)Anormoperationon thequaternionalgebra.

Usage notes

(mathematics,linear algebra):

• The array's dimensionality (number of indices needed to label a component) is called itsorder(alsodegreeorrank).
• Tensors operate in the context of avector spaceand thus within a choice ofbasis vectors,but, because they express relationships between vectors, must be independent of any given choice of basis. This independence takes the form of a law ofcovariantand/orcontravariant transformationthat relates the arrays computed in different bases. The precise form of the transformation law determines thetype(orvalence) of the tensor. Thetensor typeis a pair of natural numbers (n,m), wherenis the number ofcontravariant indicesandmthe number ofcovariant indices.The total order of the tensor is the sumn+m.

Derived terms

• tensor algebra
• tensor field
• tensorial
• tensor operator
• tensor product
• tonic tensor tympani syndrome

Translations

muscle

• Bulgarian:флексорm(fleksor)
• Chinese:

  Mandarin:Trương cơ／Trương cơ(zhāngjī)

• Finnish:jännittäjälihas
• Italian:tensore(it)m
• Tagalog:kalamnang pamatak

image of a tuple under a tensor product map

• Czech:tenzorm
• Esperanto:tensoro
• Finnish:tensori(fi)
• German:Tensor(de)m
• Hindi:प्रदिश(pradiś)
• Icelandic:þinur(is)m
• Italian:tensore(it)m
• Norwegian:tensor
• Polish:tensor(pl)m
• Romanian:tensor(ro)m
• Serbo-Croatian:tenzor(sh)m
• Swedish:tensor(sv)c
• Tagalog:katuganhan,katuganuhan
• Turkish:tensör

function of several variables

• Arabic:مُوتَرm(mūtar)
• Finnish:tensori(fi)
• French:tenseur(fr)m
• German:Tensor(de)m
• Italian:tensore(it)m
• Norwegian:tensor
• Polish:tensor(pl)m
• Serbo-Croatian:tenzor(sh)m
• Swedish:tensor(sv)c
• Tagalog:katuganhan,katuganuhan
• Turkish:tensör

matrix of matrices

• Arabic:مُوتَرm(mūtar)
• Bulgarian:тензорm(tenzor)
• Finnish:tensori(fi)
• German:Tensor(de)m
• Greek:τανυστήςm(tanystís)
• Italian:tensore(it)m
• Norwegian:tensor
• Polish:tensor(pl)m
• Serbo-Croatian:tenzor(sh)m
• Swedish:tensor(sv)c
• Tagalog:katuganhan,katuganuhan
• Turkish:tensör

Verb

tensor(third-person singular simple presenttensors,present participletensoring,simple past and past participletensored)

1. Tocomputethetensor productof twotensorsor algebraic structures.

References

• “tensor”,inLexico,Dictionary.com;Oxford University Press,2019–2022.
• “tensor”,inMerriam-Webster Online Dictionary,Springfield, Mass.:Merriam-Webster,1996–present.

Anagrams

• noters,tenors,sterno-,Trones,nestor,Stoner,Treons,rest on,trones,Sterno,Nortes,toners,Reston,Nestor,stoner,-setron

Dutch

Etymology

Ultimately or directly fromLatintensor.

Pronunciation

• IPA^(key):/ˈtɛn.zɔr/,/ˈtɛn.sɔr/

• Audio:

  (file)

• Hyphenation:ten‧sor
• Rhymes:-ɛnzɔr

Noun

tensorm(pluraltensoren)

1. (mathematics,linear algebra)tensor

Derived terms

• tensoralgebra

Latin

Etymology

Fromtendō(“stretch, distend, extend”)+‎-tor(agent suffix).

Pronunciation

• (Classical Latin)IPA^(key):/ˈten.sor/,[ˈt̪ẽːs̠ɔr]
• (modern Italianate Ecclesiastical)IPA^(key):/ˈten.sor/,[ˈt̪ɛnsor]

Noun

tensorm(genitivetensōris);third declension(New Latin)

1. that whichstretches

Inflection

Third-declensionnoun.

Case	Singular	Plural
Nominative	tensor	tensōrēs
Genitive	tensōris	tensōrum
Dative	tensōrī	tensōribus
Accusative	tensōrem	tensōrēs
Ablative	tensōre	tensōribus
Vocative	tensor	tensōrēs

Descendants

• →English:tensor

Polish

Etymology

(Thisetymologyis missing or incomplete. Please add to it, or discuss it at theEtymology scriptorium.)

Pronunciation

• IPA^(key):/ˈtɛn.sɔr/

• Audio:

  (file)

• Rhymes:-ɛnsɔr
• Syllabification:ten‧sor

Noun

tensorminan(related adjectivetensorowy)

1. (mathematics,physics)tensor

Declension

Declension oftensor

	singular	plural
nominative	tensor	tensory
genitive	tensora	tensorów
dative	tensorowi	tensorom
accusative	tensor	tensory
instrumental	tensorem	tensorami
locative	tensorze	tensorach
vocative	tensorze	tensory

Further reading

• tensorin Polish dictionaries at PWN

Portuguese

Etymology

BorrowedfromFrenchtenseur.

Pronunciation

• (Brazil)IPA^(key):/tẽˈsoʁ/[tẽˈsoh]

• (Brazil)IPA^(key):/tẽˈsoʁ/[tẽˈsoh]
  • (São Paulo)IPA^(key):/tẽˈsoɾ/
  • (Rio de Janeiro)IPA^(key):/tẽˈsoʁ/[tẽˈsoχ]
  • (Southern Brazil)IPA^(key):/tẽˈsoɻ/

• (Portugal)IPA^(key):/tẽˈsoɾ/

• (Portugal)IPA^(key):/tẽˈsoɾ/
  • (Southern Portugal)IPA^(key):/tẽˈso.ɾi/

• Rhymes:(Portugal, São Paulo)-oɾ,(Brazil)-oʁ
• Hyphenation:ten‧sor

Adjective

tensor(femininetensora,masculine pluraltensores,feminine pluraltensoras)

1. tensing;tensile

Noun

tensorm(pluraltensores)

1. (mathematics)tensor

Romanian

Etymology

BorrowedfromFrenchtenseurorGermanTensor.

Noun

tensorm(pluraltensori)

1. (mathematics)tensor

Declension

Declension oftensor

	singular		plural
	indefinite articulation	definite articulation	indefinite articulation	definite articulation
nominative/accusative	(un)tensor	tensorul	(niște)tensori	tensorii
genitive/dative	(unui)tensor	tensorului	(unor)tensori	tensorilor
vocative	tensorule		tensorilor

Spanish

Pronunciation

• IPA^(key):/tenˈsoɾ/[t̪ẽnˈsoɾ]
• Rhymes:-oɾ
• Syllabification:ten‧sor

Adjective

tensor(femininetensora,masculine pluraltensores,feminine pluraltensoras)

1. tensing;tensile

Noun

tensorm(pluraltensores)

1. tensor

Derived terms

• tensor del tímpano
• tensor métrico

Further reading

• “tensor”,inDiccionario de la lengua española,Vigésima tercera edición,Real Academia Española,2014

Swedish

Noun

tensorc

1. (mathematics)tensor;a function which is linear in all variables

Declension

Declension oftensor
	Singular		Plural
	Indefinite	Definite	Indefinite	Definite
Nominative	tensor	tensorn	tensorer	tensorerna
Genitive	tensors	tensorns	tensorers	tensorernas

Anagrams

• noters,ortens,rosten,rotens,sorten,toners