View source for Linear

{{also|LINEAR|Linear|lineär}}
==English==
{{wikipedia}}

===Etymology===
From {{bor|en|la|līneāris}}, from {{m|la|līnea||line}} + {{m|la|-āris}} (adjectival suffix), equivalent to {{suf|en|line|ar}}. {{doublet|en|lineal}}.

===Pronunciation===
* {{IPA|en|/ˈlɪn.i.əɹ/}}
** {{audio|en|En-us-linear.ogg|a=US}}
* {{IPA|en|/ˈliːnijə(ɾ)/|a=South Asia}}

===Adjective===
{{enum|en|constant|quadratic|[[Appendix:English polynomial degrees|polynomial degrees]]}}
{{en-adj}}

# Having the form of a [[line]]; [[straight]] or roughly straight; following a direct course.
#* {{quote-journal|1=en|year=2019|author=Li Huang; James Lambert|title=Another Arrow for the Quiver: A New Methodology for Multilingual Researchers|journal=Journal of Multilingual and Multicultural Development|doi=10.1080/01434632.2019.1596115|page=4|text=The route taken does not have to be a perfectly straight line, just so long as it is '''linear''' and is followed consistently for each transect taken.}}
# Of or relating to lines.
# Made, or designed to be used, in a [[step-by-step]], [[sequential]] manner.
#: {{ux|en|a '''linear''' medium}}
# {{lb|en|botany|of leaves}} Long and narrow, with nearly [[parallel]] sides.
# {{lb|en|mathematics}} ({{non-gloss|of [[polynomial]]s or polynomial [[equation]]s}})
## {{lb|en|of a polynomial}} Having [[degree]] one; that is, being of the form <math> a_1x_1 + a_2x_2 + \cdots + a_nx_n +b</math>, where each <math>x_i</math> is a [[variable]]. See also {{pedia|Linearity#Linear_polynomials|Linear polynomials}}
##: {{ux|en|<math>4x + 5y + \frac{1}{2}z</math> is a linear polynomial, but <math>4xy + \frac{1}{2}z</math> and <math>4x + z^2</math> are not.}}
## {{lb|en|of a polynomial equation}} Involving only linear polynomials. See also {{pedia|Linear equation}}
##: {{ux|en|The [[graph]] of the linear equation <math> y = ax + b </math> is a straight line with [[slope]] <math>a</math> and [[y-intercept]] <math>b</math>}}
# {{lb|en|mathematics}} ({{non-gloss|of [[function]]s or [[map]]s}})
## {{lb|en|of a [[function]] between [[vector space]]s}} An [[additive]], [[homogeneous function|homogeneous]] [[mapping]]; that is, a function <math>f:V \to W</math> is '''linear''' if it [[distribute]]s over [[vector]] addition (<math>f(\mathbf{v} + \mathbf{w}) = f(\mathbf{v}) + f(\mathbf{w})</math>) and respects [[scalar]] multiplication (<math>f(c\mathbf{v}) = cf(\mathbf{v})</math>). If <math>V</math> and <math>W</math> are vector spaces over a [[field]] <math>K</math>, <math>f</math> may also be called a''' <math>K</math>-linear''' map. See also {{pedia|linear map}}
##: {{ux|en|The map <math>f:\mathbb{R}^3 \to \mathbb{R}^2</math> taking <math>(x,y,z) \mapsto (x+y+z,x-y+3z)</math> is a linear map.}}
## {{lb|en|of a [[function]] over a [[module]]}} A module [[homomorphism]]; that is, a [[group]] homomorphism that commutes with scalar multiplication. See also {{pedia|Module homomorphism}}
# {{lb|en|physics}} A type of [[length]] measurement involving only one spatial [[dimension]] {{qualifier|as opposed to area or volume}}.
#: {{ux|en|a [[linear meter]]}}

{{C|en|Polynomials|Curves|One}}

====Synonyms====
* {{l|en|linelike}}

====Antonyms====
* {{l|en|nonlinear}}

====Coordinate terms====
* {{sense|pertaining to length}} {{l|en|areal}}, {{l|en|spacial}}, {{l|en|spatial}}
* {{sense|one-dimensional unit}} {{l|en|cubic}}, {{l|en|square}}

====Derived terms====
{{col3|en|linear elasticity
|curvilinear
|interlineal|linear congruential generator|linear time-invariant|linear time-varying|non-linear text
|interlinear
|lineal|antilinear|basolinear|bilinear|circumlinear|colinear|collinear|crosslinear|hyperlinear|isolinear|linearise|linearism|linearithmic|linearity|linearization|linearize|linearly|linearoid|lineartuberculate|matrilinear|linear map|monolinear|multilinear|ortholinear|paralinear|patrilinear|plurilinear|polylinear|pseudolinear|quadrilinear|quasilinear|semilinear|sesquilinear|sublinear|superlinear|translinear|trilinear|ultralinear|unilinear|vertilinear
|supralinear
|linear algebra
|linear foot
|linear meter,linear metre
|general linear group|linear algebraic|linear algebraic group|linear channel|linear combination|linear density|linear dependence|linear equation|linear form|linear function|linear functional|linear group|linear independence|linear logic|linear motor|linear operator|linear order|linear pair|linear park|linear perspective|linear programming|linear relative|linear space|linear span|linear subspace|linear sum|linear system|linear television|linear time|linear transformation|linear triplet|linear TV|log-linear|non-linear|numerical linear algebra|piecewise linear|piecewise-linear|positive linear functional|rectified linear unit|special linear group|spherical linear interpolation|linear regression
}}

====Translations====
{{trans-top|having the form of a line}}
* Afrikaans: {{t|af|lineêr}}
* Belarusian: {{t|be|ліне́йны}}
* Bulgarian: {{t|bg|линеен}}
* Catalan: {{t+|ca|lineal}}, {{t+|ca|linear}}
* Chinese:
*: Mandarin: {{t+|cmn|线性|tr=xianxing}}
* Danish: {{t+|da|lige}}, {{t|da|lineær}}
* Dutch: {{t+|nl|lineair}}
* Faroese: {{t|fo|linjurættur}}
* Finnish: {{t+|fi|suoraviivainen}}
* French: {{t+|fr|linéaire}}
* Galician: {{t+|gl|lineal}}, {{t|gl|linear}}
* German: {{t+|de|linear}}
* Greek: {{t+|el|γραμμικός}}
*: Ancient: {{t|grc|γραμμικός}}
* Hungarian: {{t+|hu|vonalas}}
* Icelandic: {{t|is|línulegur}}
* Indonesian: {{t+|id|linear}}, {{t+|id|linier}}
* Italian: {{t+|it|lineare}}
* Latin: {{t|la|linearis}}
* Norwegian: {{t|no|lineær}}
* Polish: {{t+|pl|linearny}}, {{t+|pl|liniowy}}
* Portuguese: {{t+|pt|linear}}
* Russian: {{t+|ru|лине́йный}}
* Spanish: {{t+|es|lineal}}
* Swedish: {{t+|sv|linjär}}
* Turkish: {{t+|tr|doğrusal}}, {{t+|tr|lineer}}
* Ukrainian: {{t|uk|ліні́йний}}
{{trans-bottom}}

{{trans-top|of or relating to lines}}
* Finnish: {{t+|fi|suoraviivainen}}
* Latin: {{t|la|linearis}}
* Malay: {{t+|ms|garis}}, {{t+|ms|garisan}}, {{t|ms|kegarisan}}, {{t|ms|kegarisanan}}, {{t|ms|linear}}
* Polish: {{t+|pl|linearny}}, {{t+|pl|liniowy}}
* Spanish: {{t+|es|lineal}}
{{trans-bottom}}

{{trans-top|made in a step-by-step manner}}
* Finnish: {{t+|fi|suoraviivainen}}, {{t+|fi|johdonmukainen}}
* Russian: {{t+|ru|после́довательный}}
{{trans-bottom}}

{{trans-top|botany, of leaves: long and narrow}}
* Finnish: {{t+|fi|tasasoukka}}
* Spanish: {{t+|es|lineal}}
{{trans-bottom}}

{{trans-top|in mathematics, of first-degree polynomial}}
* Afrikaans: {{t|af|lineêr}}
* Bulgarian: {{t|bg|линеен}}
* Czech: {{t+|cs|lineární}}
* Danish: {{t|da|lineær}}
* Finnish: {{t+|fi|lineaarinen}}
* French: {{t+|fr|linéaire}}
* German: {{t+|de|linear}}
* Greek: {{t+|el|γραμμικός}}
* Italian: {{t+|it|lineare}}
* Norwegian: {{t|no|lineær}}
* Polish: {{t+|pl|linearny}}, {{t+|pl|liniowy}}
* Portuguese: {{t+|pt|linear}}
* Russian: {{t+|ru|лине́йный}}
* Spanish: {{t+|es|lineal}}
* Swedish: {{t+|sv|linjär}}, {{t+|sv|lineär}}
{{trans-bottom}}

{{trans-top|physics: involving only one dimension}}
* Afrikaans: {{t|af|lineêr}}
* Finnish: {{t+|fi|lineaarinen}}
* German: {{t+|de|linear}}
* Polish: {{t+|pl|linearny}}, {{t+|pl|liniowy}}
* Russian: {{t+|ru|линейный}}, {{t+|ru|одномерный}}
* Spanish: {{t+|es|unidimensional}}
{{trans-bottom}}

{{checktrans-top}}
* French: {{qualifier|1,2}} {{t+check|fr|linéaire}}
* Japanese: {{t+check|ja|リニア|tr=rinia}}, {{t+check|ja|リンネル|tr=rinneru}}, {{t+check|ja|線形|tr=senkei 1,2}}, {{t+check|ja|一次|tr=ichiji 2,3}}
* Korean: {{t+check|ko|선형}} {{q|1,2}}, {{t+check|ko|일차}} {{q|2,3}}
{{trans-bottom}}

===Noun===
{{en-noun}}

# {{lb|en|radio slang}} {{ellipsis of|en|linear amplifier}}

===References===
* {{pedia}}
* {{R:OneLook}}
* {{R:Century 1911}}

===Anagrams===
* {{anagrams|en|a=aeilnr|Arline|Erlian|Irelan|Lanier|aliner|enrail|lanier|larine|nailer|renail}}

==Catalan==

===Etymology===
{{bor+|ca|la|līneāris}}.

===Pronunciation===
* {{ca-IPA|[a(rr)]}}<!-- per GDLC -->

===Adjective===
{{ca-adj}}

# {{l|en|linear}}
#: {{syn|ca|lineal}}

====Related terms====
* {{l|ca|línia}}

===Further reading===
* {{R:ca:IEC2}}
* {{R:ca:GDLC}}
* {{R:ca:DNV}}
* {{R:ca:DCVB}}

==Indonesian==

===Etymology===
{{internationalism|id}}, {{bor+|id|nl|lineair|t=linear|nocap=1}}, from {{der|id|fr|linéaire}}, from {{der|id|la|līneāris}}.<ref>{{cite-book|author=Nicoline van der Sijs|title=Nederlandse woorden wereldwijd|year=2010|publisher=Sdu Uitgevers|location=Den Haag|url=https://www.worldcat.org/oclc/687330964|isbn=978-90-12-58214-8|oclc=687330964}}</ref>

===Pronunciation===
* {{IPA|id|/liˈnɛar/}}
* {{rhymes|id|ar|r|s=3}}
* {{hyphenation|id|li|nè|ar}}

===Adjective===
{{id-adj|head=linèar}}

# {{alt sp|id|[[linier|linièr]]|t={{l|en|linear}}|nocap=1}}

===References===
<references/>

===Further reading===
* {{R:KBBI Daring}}

==Portuguese==

===Etymology===
{{lbor|pt|la|līneāris}}.

===Pronunciation===
{{pt-IPA|linearh}}
* {{hyphenation|pt|li|ne|ar}}

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

# {{l|en|linear}} {{gloss|having the form of a straight line}}
# {{lb|pt|mathematics}} {{l|en|linear}} {{gloss|being a first-degree polynomial}}
# {{l|en|linear}} {{gloss|made in a step-by-step, logical manner}}

====Related terms====
* {{l|pt|linha}}

===Further reading===
* {{R:pt:Priberam}}

==Romanian==

===Adjective===
{{ro-adj}}

# {{alternative form of|ro|liniar}}

====Declension====
{{ro-decl-adj}}

==Spanish==

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

===Etymology 1===
From {{der|es|la|lineāris}}.

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

# {{lb|es|botany}} {{l|en|linear}}

=====Derived terms=====
{{col|es|perspectiva linear}}

===Etymology 2===
From {{der|es|la|lineo|lineāre}}.

====Verb====
{{es-verb}}

# to [[line]]
# to [[outline]], [[mark]] out

=====Conjugation=====
{{es-conj|nocomb=1}}

=====Derived terms=====
{{col|es|lineamiento}}

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