tensor

See also: Tensor and tensör

English

Etymology

Borrowed from New Latin tensor (“that which stretches”), equivalent to tense +‎ -or. Anatomical sense from 1704. Introduced in the 1840s by William Rowan Hamilton as an algebraic quantity unrelated to the modern notion of tensor. The contemporary mathematical meaning was introduced (as German Tensor) by Woldemar Voigt (1898) and adopted in English from 1915 (in the context of general relativity), obscuring the earlier Hamiltonian sense. The mathematical object is so named because an early application of tensors was the study of materials stretching under tension. (See, for example, Cauchy stress tensor on 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 (plural tensors or (muscle) tensores)

1. (anatomy) A muscle that tightens or stretches a part, or renders it tense. [from 17th c.]

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

2. (mathematics, linear algebra, physics) A mathematical object that describes linear relations on scalars, vectors, matrices and other algebraic objects, and is represented as a multidimensional 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”, in The Feynman Lectures on Physics, volume II:

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

   1. (engineering) A multidimensional array with (at least) two dimensions.
3. (mathematics, obsolete) A norm operation on the quaternion algebra.

Usage notes

(mathematics, linear algebra):

• The array's dimensionality (number of indices needed to label a component) is called its order (also degree or rank).
  • In engineering usage the term is commonly used only for ranks of 2 (or more), contrasted with scalar and vectors.
• Tensors operate in the context of a vector space and thus within a choice of basis 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 of covariant and/or contravariant transformation that relates the arrays computed in different bases. The precise form of the transformation law determines the type (or valence) of the tensor. The tensor type is a pair of natural numbers (n, m), where n is the number of contravariant indices and m the number of covariant indices. The total order of the tensor is the sum n + m.

Derived terms

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

 

Translations

muscle

• Bulgarian: флексор m (fleksor)
• Chinese:

  Mandarin: 張肌／张肌 (zhāngjī)

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

image of a tuple under a tensor product map

• Czech: tenzor m
• 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: مُوتَر m (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: مُوتَر m (mūtar)
• Bulgarian: тензор m (tenzor)
• Finnish: tensori (fi)
• German: Tensor (de) m
• Greek: τανυστής m (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 present tensors, present participle tensoring, simple past and past participle tensored)

1. To compute the tensor product of two tensors or algebraic structures.

References

• “tensor”, in Lexico, Dictionary.com; Oxford University Press, 2019–2022.
• “tensor”, in Merriam-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 from Latin tensor.

Pronunciation

• IPA^(key): /ˈtɛn.zɔr/, /ˈtɛn.sɔr/

• Audio:

  (file)

• Hyphenation: ten‧sor
• Rhymes: -ɛnzɔr

Noun

tensor m (plural tensoren)

1. (mathematics, linear algebra) tensor

Derived terms

• tensoralgebra

Latin

Etymology

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

Pronunciation

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

Noun

tensor m (genitive tensōris); third declension (New Latin)

1. that which stretches

Inflection

Third-declension noun.

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

(This etymology is missing or incomplete. Please add to it, or discuss it at the Etymology scriptorium.)

Pronunciation

• IPA^(key): /ˈtɛn.sɔr/

• Audio:

  (file)

• Rhymes: -ɛnsɔr
• Syllabification: ten‧sor

Noun

tensor m inan (related adjective tensorowy)

1. (mathematics, physics) tensor

Declension

Declension of tensor

	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

• tensor in Polish dictionaries at PWN

Portuguese

Etymology

Borrowed from French tenseur.

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 (feminine tensora, masculine plural tensores, feminine plural tensoras)

1. tensing; tensile

Noun

tensor m (plural tensores)

1. (mathematics) tensor

Romanian

Etymology

Borrowed from French tenseur or German Tensor.

Noun

tensor m (plural tensori)

1. (mathematics) tensor

Declension

Declension of tensor

	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 (feminine tensora, masculine plural tensores, feminine plural tensoras)

1. tensing; tensile

Noun

tensor m (plural tensores)

1. tensor

Derived terms

• tensor del tímpano
• tensor métrico

 

Further reading

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

Swedish

Noun

tensor c

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

Declension

Declension of tensor

		nominative	genitive
singular	indefinite	tensor	tensors
	definite	tensorn	tensorns
plural	indefinite	tensorer	tensorers
	definite	tensorerna	tensorernas

Anagrams

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