tensor
English edit
Etymology edit
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 edit
- (Received Pronunciation) IPA(key): /ˈtɛn.sə/, /ˈtɛn.sɔː/
Audio (Southern England) (file) - (General American) IPA(key): /ˈtɛn.sɚ/, /ˈtɛn.sɔɹ/
- Rhymes: -ɛnsə(ɹ)
Noun edit
tensor (plural tensors or (muscle) tensores)
- (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
- (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.
- (mathematics, obsolete) A norm operation on the quaternion algebra.
Usage notes edit
(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.
Derived terms edit
Translations edit
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Verb edit
tensor (third-person singular simple present tensors, present participle tensoring, simple past and past participle tensored)
- To compute the tensor product of two tensors or algebraic structures.
References edit
- “tensor”, in Lexico, Dictionary.com; Oxford University Press, 2019–2022.
- “tensor”, in Merriam-Webster Online Dictionary, Springfield, Mass.: Merriam-Webster, 1996–present.
Anagrams edit
Dutch edit
Etymology edit
Ultimately or directly from Latin tensor.
Pronunciation edit
Noun edit
tensor m (plural tensoren)
Derived terms edit
Latin edit
Etymology edit
From tendō (“stretch, distend, extend”) + -tor (agent suffix).
Pronunciation edit
- (Classical) IPA(key): /ˈten.sor/, [ˈt̪ẽːs̠ɔr]
- (modern Italianate Ecclesiastical) IPA(key): /ˈten.sor/, [ˈt̪ɛnsor]
Noun edit
tensor m (genitive tensōris); third declension (New Latin)
- that which stretches
Inflection edit
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 edit
- → English: tensor
Polish edit
Etymology edit
(This etymology is missing or incomplete. Please add to it, or discuss it at the Etymology scriptorium.)
Pronunciation edit
Noun edit
tensor m inan (related adjective tensorowy)
Declension edit
Further reading edit
- tensor in Polish dictionaries at PWN
Portuguese edit
Etymology edit
Borrowed from French tenseur.[1]
Pronunciation edit
Adjective edit
tensor (feminine tensora, masculine plural tensores, feminine plural tensoras)
Noun edit
tensor m (plural tensores)
References edit
Romanian edit
Etymology edit
Borrowed from French tenseur or German Tensor.
Noun edit
tensor m (plural tensori)
Declension edit
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 edit
Pronunciation edit
Adjective edit
tensor (feminine tensora, masculine plural tensores, feminine plural tensoras)
Noun edit
tensor m (plural tensores)
Derived terms edit
Further reading edit
- “tensor”, in Diccionario de la lengua española, Vigésima tercera edición, Real Academia Española, 2014
Swedish edit
Noun edit
tensor c
- (mathematics) tensor; a function which is linear in all variables
Declension edit
Declension of tensor | ||||
---|---|---|---|---|
Singular | Plural | |||
Indefinite | Definite | Indefinite | Definite | |
Nominative | tensor | tensorn | tensorer | tensorerna |
Genitive | tensors | tensorns | tensorers | tensorernas |