This questions has been stumping me for a few days now. But the questions asks how I could define an inner product for a vector space V such that all the vectors in a basis C are orthonormal.
So all vectors in a basis will have inner products equal to 0 (orthogonal), but how can I define another inner product to make sure that their length is 1, without dividing the inner product by the inner product..
I can't really visualize this. Some insight would be appreciated.