tensor

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tensor (disambiguation)

Wikipedia

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 )

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

• Audio (Southern England):

  (file)

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

tensor (plural tensors or (muscle) tensores)

1. (anatomy) A muscle that tightens or stretches a part, or renders it tense.

   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. ^[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 ${\displaystyle \alpha _{ij}}$ 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.

(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.

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.

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

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

Ultimately or directly from Latin tensor.

• IPA^(key): /ˈtɛn.zɔr/, /ˈtɛn.sɔr/

• Audio:

  (file)

• Hyphenation: ten‧sor
• Rhymes: -ɛnzɔr

tensor m (plural tensoren)

1. (mathematics, linear algebra) tensor

• tensoralgebra

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

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

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

1. that which stretches

Third-declension noun.

• → English: tensor

Polish Wikipedia has an article on:

tensor

Wikipedia ^pl

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

• IPA^(key): /ˈtɛn.sɔr/

• Audio:

  (file)

• Rhymes: -ɛnsɔr
• Syllabification: ten‧sor

tensor m inan (related adjective tensorowy)

1. (mathematics, physics) tensor

• tensor in Polish dictionaries at PWN

Borrowed from French tenseur.^[1]

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

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

1. tensing; tensile

tensor m (plural tensores)

1. (mathematics) tensor

Borrowed from French tenseur or German Tensor.

tensor m (plural tensori)

1. (mathematics) tensor

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

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

1. tensing; tensile

tensor m (plural tensores)

1. tensor

• “tensor”, in Diccionario de la lengua española [Dictionary of the Spanish Language] (in Spanish), online version 23.8, Royal Spanish Academy [Spanish: Real Academia Española], 2024 December 10

tensor c

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

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