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Homework Statement
(X,<,>) is a inner product space over R
{ei}i in N is an orthonormal set in X
Show that if every element u in X can be written as a linear combination
u = [tex]\sum_{i=1}^\infty a_i e_i [/tex] then {ei}i in N is a basis for X
Homework Equations
Let {ei}be a sequence of elements in a normed vector
space V . We say that {en} is a basis for V if for each x in V there is a
unique sequence {an} from K such that:
x = [tex] \sum_{n=1}^{\infty} a_i e_i [/tex]
The Attempt at a Solution
I'm not sure what I have to prove. Is not the definition of a basis given in the question?