1. ## vector space example

let X be any non-empty set.
Let G be the set of all real valued functions defined on X.
Let vector addition be the usual addition of real valued function, and scalar multiplication be the usual multiplication of real valued function by real numbers.
G is a real vector space.

I don't really understand it.
Can you please give me an example of it? Thank you very much.

2. Originally Posted by happystudent
let X be any non-empty set.
Let G be the set of all real valued functions defined on X.
Let vector addition be the usual addition of real valued function, and scalar multiplication be the usual multiplication of real valued function by real numbers. G is a real vector space.
I don't really understand it.
What don’t you understand?
Can you give the set of requirements necessary to have a vector space?
Is the set of functions closed with respect to addition and scalar multiplication?
Can you finish off the list of requirements?