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See also: Tensor and tensör

English

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English Wikipedia has an article on:
Wikipedia

Etymology

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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)[1] 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

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Noun

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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.][2]
    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   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

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(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

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Translations

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Verb

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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

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  1. ^ W. Voigt, Die fundamentalen physikalischen Eigenschaften der Krystalle in elementarer Darstellung, Leipzig, Germany: Veit & Co., 1898, p. 20.
  2. ^ Rowland, Todd and Weisstein, Eric W., "Tensor", Wolfram MathWorld.

Anagrams

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Dutch

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Etymology

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Ultimately or directly from Latin tensor.

Pronunciation

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

Noun

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tensor m (plural tensoren)

  1. (mathematics, linear algebra) tensor

Derived terms

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Latin

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Etymology

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

Pronunciation

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Noun

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

  1. that which stretches

Inflection

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Third-declension noun.

singular plural
nominative tensor tensōrēs
genitive tensōris tensōrum
dative tensōrī tensōribus
accusative tensōrem tensōrēs
ablative tensōre tensōribus
vocative tensor tensōrēs

Descendants

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  • English: tensor

Polish

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Polish Wikipedia has an article on:
Wikipedia pl

Etymology

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

Pronunciation

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Noun

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tensor m inan (related adjective tensorowy)

  1. (mathematics, physics) tensor

Declension

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Further reading

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  • tensor in Polish dictionaries at PWN

Portuguese

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Etymology

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Borrowed from French tenseur.[1]

Pronunciation

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

Adjective

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

  1. tensing; tensile

Noun

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tensor m (plural tensores)

  1. (mathematics) tensor

References

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  1. ^ tensor”, in Dicionário Priberam da Língua Portuguesa (in Portuguese), Lisbon: Priberam, 20082024

Romanian

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Etymology

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Borrowed from French tenseur or German Tensor.

Noun

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tensor m (plural tensori)

  1. (mathematics) tensor

Declension

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singular plural
indefinite definite indefinite definite
nominative-accusative tensor tensorul tensori tensorii
genitive-dative tensor tensorului tensori tensorilor
vocative tensorule tensorilor

Spanish

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Pronunciation

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

Adjective

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

  1. tensing; tensile

Noun

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tensor m (plural tensores)

  1. tensor

Derived terms

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Further reading

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Swedish

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Noun

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tensor c

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

Declension

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Anagrams

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