View source for Tensor

{{also|Tensor|tensör}}
==English==
{{wp|tensor (disambiguation)}}

===Etymology===
Borrowed from {{bor|en|NL.|tensor||that which stretches}}, equivalent to {{af|en|tense|-or}}. Anatomical sense from 1704.
Introduced in the 1840s by {{coin|en|William Rowan Hamilton|notext=1}} as an algebraic quantity unrelated to the modern notion of tensor.
The contemporary mathematical meaning was introduced (as {{bor|en|de|Tensor}}) by Woldemar Voigt (1898)<ref>W. Voigt, ''Die fundamentalen physikalischen Eigenschaften der Krystalle in elementarer Darstellung'', Leipzig, Germany: Veit & Co., 1898, p. 20.</ref> 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, {{pedia|Cauchy stress tensor}})

===Pronunciation===
* {{IPA|en|/ˈtɛn.sə/|/ˈtɛn.sɔː/|a=RP}}
* {{audio|en|LL-Q1860 (eng)-Vealhurl-tensor.wav|a=Southern England}}
* {{IPA|en|/ˈtɛn.sɚ/|/ˈtɛn.sɔɹ/|a=GA}}
* {{rhymes|en|ɛnsə(ɹ)|s=2}}

===Noun===
{{en-noun|+|tensores|pl2qual=muscle}}

# {{lb|en|muscle}} A [[muscle]] that [[tighten]]s or [[stretch]]es a part, or renders it [[tense]]. {{defdate|from 17th c.}}
#: {{hypo|en|tensor fasciae latae|tensor tympani|tensor veli palatini}}
# {{lb|en|mathematics|linear algebra|physics}} A [[mathematical]] object that describes [[linear]] relations on [[scalar]]s, [[vector]]s, [[matrix|matrices]] and other [[algebraic]] objects, and is represented as a [[multidimensional array]]. {{defdate|from 18th c.}}<ref>Rowland, Todd and Weisstein, Eric W., [http://mathworld.wolfram.com/Tensor.html "Tensor"], Wolfram MathWorld.</ref>
#: {{hyper|en|function}}
#: {{hypo|en|duotensor|eigentensor|Faraday tensor|hypertensor|metric tensor|pseudotensor|subtensor|supertensor|vector|Weyl tensor|zero tensor}}
#* {{quote-book|en|year=1963|author=w:Richard Feynman|title=w:The Feynman Lectures on Physics|volume=II|chapter=Chapter 31, Tensors|chapterurl=http://www.feynmanlectures.caltech.edu/II_31.html|text=The '''tensor''' <math>\alpha_{ij}</math> 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.}}
## {{lb|en|engineering}} A [[multidimensional array]] with (at least) two dimensions. 
# {{lb|en|mathematics|obsolete}} A [[norm]] [[operation]] on the [[quaternion]] [[algebra]].

====Usage notes====
{{sense|mathematics|linear algebra}}
* The array's dimensionality (number of indices needed to label a component) is called its {{m|en|order}} (also {{m|en|degree}} or {{m|en|rank}}).
** In engineering usage the term is commonly used only for ranks of 2 (or more), contrasted with [[scalar]] and [[vector]]s.  
* Tensors operate in the context of a [[vector space]] and thus within a choice of {{w|Basis (linear algebra)|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 {{w|covariant transformation|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 {{m|en|tensor type}} is a pair of natural numbers (''n'', ''m''), where ''n'' is the number of {{m|en|contravariant index|contravariant indices}} and ''m'' the number of {{m|en|covariant index|covariant indices}}. The total order of the tensor is the sum ''n'' + ''m''.

====Derived terms====
{{col2|en
|tensor algebra
|tensor field
|tensor operator
|tensor product
|tensorial| tonic tensor tympani syndrome}}

====Translations====
{{trans-top|muscle}}
* Bulgarian: {{t|bg|флексор|m}}
* Chinese:
*: Mandarin: {{t|cmn|張肌|tr=zhāngjī}}
* Finnish: {{t|fi|jännittäjälihas}}
* Italian: {{t+|it|tensore|m}}
* Polish: {{t|pl|napinacz|m}}
* Tagalog: {{t|tl|kalamnang pamatak}}
{{trans-bottom}}

{{trans-top|image of a tuple under a tensor product map}}
* Czech: {{t|cs|tenzor|m}}
* Esperanto: {{t|eo|tensoro}}
* Finnish: {{t+|fi|tensori}}
* German: {{t+|de|Tensor|m}}
* Hindi: {{t|hi|प्रदिश}}
* Icelandic: {{t+|is|þinur|m}}
* Italian: {{t+|it|tensore|m}}
* Norwegian: {{t|no|tensor}}
* Polish: {{t+|pl|tensor|m}}
* Romanian: {{t+|ro|tensor|m}}
* Serbo-Croatian: {{t+|sh|tenzor|m}}
* Swedish: {{t+|sv|tensor|c}}
* Tagalog: {{t|tl|katuganhan}}, {{t|tl|katuganuhan}}
* Turkish: {{t|tr|tensör}}
{{trans-bottom}}

{{trans-top|function of several variables}}
* Arabic: {{t|ar|موتر|alt=مُوتَر|m}}
* Finnish: {{t+|fi|tensori}}
* French: {{t+|fr|tenseur|m}}
* German: {{t+|de|Tensor|m}}
* Italian: {{t+|it|tensore|m}}
* Norwegian: {{t|no|tensor}}
* Polish: {{t+|pl|tensor|m}}
* Serbo-Croatian: {{t+|sh|tenzor|m}}
* Swedish: {{t+|sv|tensor|c}}
* Tagalog: {{t|tl|katuganhan}}, {{t|tl|katuganuhan}}
* Turkish: {{t|tr|tensör}}
{{trans-bottom}}

{{trans-top|matrix of matrices}}
* Arabic: {{t|ar|موتر|alt=مُوتَر|m}}
* Bulgarian: {{t|bg|тензор|m}}
* Finnish: {{t+|fi|tensori}}
* German: {{t+|de|Tensor|m}}
* Greek: {{t|el|τανυστής|m|sc=Grek}}
* Italian: {{t+|it|tensore|m}}
* Norwegian: {{t|no|tensor}}
* Polish: {{t+|pl|tensor|m}}
* Serbo-Croatian: {{t+|sh|tenzor|m}}
* Swedish: {{t+|sv|tensor|c}}
* Tagalog: {{t|tl|katuganhan}}, {{t|tl|katuganuhan}}
* Turkish: {{t|tr|tensör}}
{{trans-bottom}}

===Verb===
{{en-verb}}

# To [[compute]] the [[tensor product]] of two [[#Noun|tensor]]s or algebraic structures.

===References===
* {{R:Lexico}}
* {{R:MWO}}
<references/>

===Anagrams===
* {{anagrams|en|a=enorst|noters|tenors|sterno-|Trones|nestor|Stoner|Treons|rest on|trones|Sterno|Nortes|toners|Reston|Nestor|stoner|-setron}}

==Dutch==

===Etymology===
Ultimately or directly from {{der|nl|la|tensor}}.

===Pronunciation===
* {{IPA|nl|/ˈtɛn.zɔr/|/ˈtɛn.sɔr/}}
* {{audio|nl|Nl-tensor.ogg}}
* {{hyphenation|nl|ten|sor}}
* {{rhyme|nl|ɛnzɔr}}

===Noun===
{{nl-noun|m|-:en|-}}

# {{lb|nl|mathematics|linear algebra}} {{l|en|tensor}}

====Derived terms====
* {{l|nl|tensoralgebra}}

==Latin==

===Etymology===
From {{af|la|tendō|-tor|t1=stretch, distend, extend|pos2=agent suffix}}.

===Pronunciation===
* {{la-IPA}}

===Noun===
{{la-noun|tensor<3>}} {{tlb|la|New Latin}}

# that which [[stretch]]es

====Inflection====
{{la-ndecl|tensor<3>}}

====Descendants====
* {{desc|en|tensor|bor=1}}

==Polish==
{{wp|lang=pl}}

===Etymology===
{{rfe|pl}}

===Pronunciation===
{{pl-pr|a=LL-Q809 (pol)-Poemat-tensor.wav}}

===Noun===
{{pl-noun|m-in|adj=tensorowy}}

# {{lb|pl|mathematics|physics}} {{l|en|tensor}}

====Declension====
{{pl-decl-noun-m-in|gens=tensora}}

===Further reading===
* {{R:pl:PWN}}

==Portuguese==

===Etymology===
{{bor+|pt|fr|tenseur}}.<ref>{{R:pt:Priberam}}</ref>

===Pronunciation===
{{pt-IPA}}
* {{rhymes|pt|oɾ|q1=Portugal, São Paulo|oʁ|q2=Brazil|s=2}}
* {{hyph|pt|ten|sor}}

===Adjective===
{{pt-adj}}

# [[tensing]]; [[tensile]]

===Noun===
{{pt-noun|m}}

# {{lb|pt|mathematics}} {{l|en|tensor}}

===References===
<references/>

==Romanian==

===Etymology===
{{bor+|ro|fr|tenseur}} or {{bor|ro|de|Tensor}}.

===Noun===
{{ro-noun|m|tensori}}

# {{lb|ro|mathematics}} {{l|en|tensor}}

====Declension====
{{ro-noun-m}}

==Spanish==

===Pronunciation===
{{es-pr}}

===Adjective===
{{es-adj}}

# [[tensing]]; [[tensile]]

===Noun===
{{es-noun|m}}

# {{l|en|tensor}}

====Derived terms====
{{col|es
|tensor del tímpano
|tensor métrico
}}

===Further reading===
* {{R:es:DRAE}}

==Swedish==

===Noun===
{{sv-noun|c}}

# {{lb|sv|mathematics}} {{l|en|tensor}}; a function which is linear in all variables

====Declension====
{{sv-infl-noun-c-r|3=tensore}}

===Anagrams===
* {{anagrams|sv|a=enorst|noters|ortens|rosten|rotens|sorten|toners}}