If F is an orthonormal basis in an inner product space X can

If F is an orthonormal basis in an inner product space X, can we represent every x element X as a linear combination of elements of F? (By definition, a linear combination consists of finitely many terms.)

Solution

Yes. By definition, a basis is a set of vectors such that every element in the vector space can be written as a linear combination of the vectors in the set. There\'s not much more to this question.