In mathematics, more specifically in functional analysis, a positive linear functional on an ordered vector space {\displaystyle } is a linear functional f {\displaystyle f} on V {\displaystyle V} so that for all positive elements v ∈ V, {\displaystyle v\in V,} that is v ≥ 0, {\displaystyle v\geq 0,} it holds that In other words, a positive linear functional is guaranteed to take nonnegative values for positive elements. Wikipedia