I'm given the inner product:
And I'm asked to find the orthonormal basis in respect of the above inner product that results from the normal basis $B=(e_1,e_2,e_3),$ $e_1=(1,0,0),e_2=(0,1,0), e_3=(0,0,1)$
My thought was to use the Gram-Schmidt process but use the given inner product to calculate the projections. However when I did so I ended up with the same vectors $e_1,e_2,e_3$ so the exact same basis...
I'm I doing somthing wrong or does the basis just stay the same?