A _linear functional_, $F$, is a [Linear map](Linear%20map.md) from a [vector space,](Vector%20spaces.md) $\mathcal{V}$ to number field $\mathbb{F}.$ --- # Proofs and Examples --- # Recommended reading For a definition of a [Linear functional](Linear%20functional.md) that most closely follows the definition given here see * [Axler S., Gerhing F.W., Ribet K.A. _Linear Algebra Done Right_, Springer, 2nd edition, 1997](Axler%20S.,%20Gerhing%20F.W.,%20Ribet%20K.A.%20Linear%20Algebra%20Done%20Right,%20Springer,%202nd%20edition,%201997.md) pgs. 117. %%Expand this whole thing for the perspective of functional analysis using Folland's real analysis textbook.%% #MathematicalFoundations/Analysis/FunctionalAnalysis #MathematicalFoundations/Analysis/Functionals #MathematicalFoundations/Algebra/AbstractAlgebra/LinearAlgebra