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 Math Emeritus Sci Advisor Thanks PF Gold P: 38,705 Well, what have you done on this? Do you know the definition of "Linear Vector Space"? If so, you just need to show that this satisfies all of the requirements in that definition. Assuming that addition and scalar multiplication are just ordinary addition of functions and multiplication by numbers, you don't need to show things like "addition is commutative" or the distributive law- those are naturally true.