tensor

See also: Tensor and tensör

English

Etymology

From (deprecated template usage) [etyl]  tensor (“that which stretches”). Anatomical sense from 1704. In the 1840s introduced 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.

Pronunciation

• Hyphenation: ten‧sor
• Rhymes: -ɛnsə(ɹ)

Noun

tensor (plural tensors)

1. (anatomy) A muscle that stretches a part, or renders it tense.
2. (mathematics, linear algebra, physics) A mathematical object that describes linear relations on scalars, vectors, matrices and other tensors, and is represented as a multidimensional array.
   • 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.

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).
• 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.

Hypernyms

• function

Hyponyms

• hypertensor
• supertensor
• vector

Derived terms

• Cauchy stress tensor
• Cartesian tensor
• covariant tensor
• contravariant tensor
• tensor algebra
• tensor field
• tensor operator
• tensor product

Related terms

• tensorial

Translations

muscle

• Finnish: jännittäjälihas
• Italian: tensore (it) m
• (deprecated template usage) {{trans-mid}}
• Tagalog: kalamnang pamatak

(mathematics, physics) image of a tuple under a tensor product map

• Czech: tenzor m
• Esperanto: tensoro
• Finnish: tensori (fi)
• German: Tensor (de) m
• Icelandic: þinur (is) m
• Italian: tensore (it) m
• Norwegian: tensor
• (deprecated template usage) {{trans-mid}}
• Polish: tensor (pl) m
• Romanian: tensor (ro) m
• Serbo-Croatian: tenzor (sh) m
• Swedish: tensor (sv) c
• Tagalog: katuganhan, katuganuhan
• Turkish: tensör

(mathematics, physics) 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
• (deprecated template usage) {{trans-mid}}
• Polish: tensor (pl) m
• Serbo-Croatian: tenzor (sh) m
• Swedish: tensor (sv) c
• Tagalog: katuganhan, katuganuhan
• Turkish: tensör

(mathematics, physics) matrix of matrices

• Arabic: مُوتَر m (mūtar)
• Finnish: tensori (fi)
• German: Tensor (de) m
• Greek: τανυστής (el) m (tanystís)
• Italian: tensore (it) m
• Norwegian: tensor
• (deprecated template usage) {{trans-mid}}
• 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.

Related terms

• tensorial

Further reading

• tensor on Wikipedia.Wikipedia
• Tensor (intrinsic definition) on Wikipedia.Wikipedia
• Classical Hamiltonian quaternions on Wikipedia.Wikipedia

Anagrams

• Nestor, Nortes, Reston, Sterno, Stoner, Trones, noters, sterno-, stoner, tenors, toners, trones

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Dutch

Etymology

Ultimately or directly from Latin tensor.

Pronunciation

• IPA^(key): /ˈtɛn.zɔr/, /ˈtɛn.sɔr/
• Hyphenation: ten‧sor
• Rhymes: -ɛnzɔr

Noun

tensor m (plural tensoren)

1. (mathematics, linear algebra) tensor

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Polish

Pronunciation

• IPA^(key): //ˈtɛw̃.sɔr//

Noun

tensor m inan

1. (mathematics) 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

Derived terms

• tensorowy

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Spanish

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

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Swedish

Noun

tensor c

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

Declension

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

Anagrams

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