Consider the real inner product space $M_{2,2}(\mathbb{R})$ (the space of 2 x 2 matrices with real entries), with inner product:
(a) Find the orthonormal basis for the subspace $U$ of $M_{2,2}(\mathbb{R})$ spanned by
I understand that to find the orthanormal basis for the subspace I have to use the Gram-Schmidt process, however, Im not quite sure how to do this. I have only every used this process with vectors and I'm not sure to do it in this case.
Now, for the orthogonal projection (part b) I am also confused. I think I am supposed to do the following: $U = span${S}.
Any help with these questions would be very appreciated