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{{Multiple issues|{{refimprove|date=June 2020}}{{lead rewrite|date=June 2020|reason=The lead should be a summary of the body of the article.}}}}
In [[mathematics]], more specifically in [[functional analysis]], a '''positive linear operator''' from an [[Ordered vector space|preordered vector space]] <math>(X, \leq)</math> into a preordered vector space <math>(Y, \leq)</math> is a [[linear operator]] <math>f</math> on <math>X</math> into <math>Y</math> such that for all [[Positive element (ordered group)|positive element]]s <math>x</math> of <math>X,</math> that is <math>x \geq 0,</math> it holds that <math>f(x) \geq 0.</math>
In other words, a positive linear operator maps the positive cone of the [[Domain of a function|___domain]] into the positive cone of the [[codomain]].
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