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== Definition ==
A [[linear function]] <math>f</math> on a [[Ordered vector space|preordered vector space]] is called '''positive''' if it satisfies either of the following equivalent conditions:
# <math>x \geq 0</math> implies <math>f(x) \geq 0.</math>
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The preorder induced by the dual cone on the space of linear functionals on <math>X</math> is called the '''{{visible anchor|dual preorder}}'''.{{sfn|Narici|Beckenstein|2011|pp=139-153}}
The '''[[Order dual (functional analysis)|order dual]]''' of an ordered vector space <math>X</math> is the set, denoted by <math>X^+,</math> defined by <math>X^+ := C^* - C^*.</math>
==Canonical ordering==
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