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ordered vector space
In mathematics an ordered vector space or partially ordered vector space is a vector space equipped with a partial order which is compatible with the vector space operations.
==Definition==
Given a vector space ''V'' over the real numbers R and a partial order ≤ on the set ''V'', the pair (''V'', ≤) is called an ordered vector space if for all ''x'',''y'',''z'' in ''V'' and 0 ≤ λ in R the following two axioms are satisfied
# ''x'' ≤ ''y'' implies ''x'' + ''z'' ≤ ''y'' + ''z''
# ''y'' ≤ ''x'' implies λ ''y'' ≤ λ ''x''.
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