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.
- (engineering) A multidimensional array with (at least) two dimensions.
- (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
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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]- noters, tenors, sterno-, Trones, nestor, Stoner, Treons, rest on, trones, Sterno, Nortes, toners, Reston, Nestor, stoner, -setron
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 Latin) 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.
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]- ^ “tensor”, in Dicionário Priberam da Língua Portuguesa (in Portuguese), Lisbon: Priberam, 2008–2024
Romanian
[edit]Etymology
[edit]Borrowed from French tenseur or German Tensor.
Noun
[edit]tensor m (plural tensori)
Declension
[edit]singular | plural | ||||
---|---|---|---|---|---|
indefinite | definite | indefinite | definite | ||
nominative-accusative | tensor | tensorul | tensori | tensorii | |
genitive-dative | tensor | tensorului | 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 [Dictionary of the Spanish Language] (in Spanish), online version 23.8, Royal Spanish Academy [Spanish: Real Academia Española], 2024 December 10
Swedish
[edit]Noun
[edit]tensor c
- (mathematics) tensor; a function which is linear in all variables
Declension
[edit]Anagrams
[edit]- English terms borrowed from New Latin
- English terms derived from New Latin
- English terms suffixed with -or
- English terms coined by William Rowan Hamilton
- English coinages
- English terms borrowed from German
- English terms derived from German
- English 2-syllable words
- English terms with IPA pronunciation
- English terms with audio pronunciation
- Rhymes:English/ɛnsə(ɹ)
- Rhymes:English/ɛnsə(ɹ)/2 syllables
- English lemmas
- English nouns
- English countable nouns
- English nouns with irregular plurals
- en:Muscles
- en:Mathematics
- en:Linear algebra
- en:Physics
- English terms with quotations
- en:Engineering
- English terms with obsolete senses
- English verbs
- Dutch terms derived from Latin
- Dutch terms with IPA pronunciation
- Dutch terms with audio pronunciation
- Rhymes:Dutch/ɛnzɔr
- Dutch lemmas
- Dutch nouns
- Dutch nouns with plural in -en
- Dutch nouns with lengthened vowel in the plural
- Dutch masculine nouns
- nl:Mathematics
- nl:Linear algebra
- Latin terms suffixed with -tor
- Latin 2-syllable words
- Latin terms with IPA pronunciation
- Latin lemmas
- Latin nouns
- Latin third declension nouns
- Latin masculine nouns in the third declension
- Latin masculine nouns
- New Latin
- Polish 2-syllable words
- Polish terms with IPA pronunciation
- Polish terms with audio pronunciation
- Rhymes:Polish/ɛnsɔr
- Rhymes:Polish/ɛnsɔr/2 syllables
- Polish lemmas
- Polish nouns
- Polish masculine nouns
- Polish inanimate nouns
- pl:Mathematics
- pl:Physics
- Portuguese terms borrowed from French
- Portuguese terms derived from French
- Portuguese 2-syllable words
- Portuguese terms with IPA pronunciation
- Portuguese 3-syllable words
- Rhymes:Portuguese/oɾ
- Rhymes:Portuguese/oɾ/2 syllables
- Rhymes:Portuguese/oʁ
- Rhymes:Portuguese/oʁ/2 syllables
- Portuguese lemmas
- Portuguese adjectives
- Portuguese nouns
- Portuguese countable nouns
- Portuguese masculine nouns
- pt:Mathematics
- Romanian terms borrowed from French
- Romanian terms derived from French
- Romanian terms borrowed from German
- Romanian terms derived from German
- Romanian lemmas
- Romanian nouns
- Romanian countable nouns
- Romanian masculine nouns
- ro:Mathematics
- Spanish 2-syllable words
- Spanish terms with IPA pronunciation
- Rhymes:Spanish/oɾ
- Rhymes:Spanish/oɾ/2 syllables
- Spanish lemmas
- Spanish adjectives
- Spanish nouns
- Spanish countable nouns
- Spanish masculine nouns
- Swedish lemmas
- Swedish nouns
- Swedish common-gender nouns
- sv:Mathematics