Let M1 = [1 1] and M2 = [-3 -2]
________[1 -1]_________[ 1 2]
Consider the inner product <A,B> = trace(transpose(A)B) in the vector space R2x2 of 2x2 matrices. Use the Gram-Schmidt process to determine an orthonormal basis for the subspace of R2x2 spanned by the matrices M1 and M2.
The Attempt at a Solution
So the inner product of the 2 matrices is <M1,M2> which is [-2 0]
if I calculated it right which I think I did. But I don't what that has to do with Gram-Schmidt or how it relates to orthonormal bases for R2x2. And I know how to use Gram-Schmidt on individual vectors but not on a whole matrix so I'm pretty stuck.