I asked this question the other day but I still didn't understand it. Hopefully someone can get through to me this time.
I have a question that reads:
Diagonalize the quadratic form A(x,y) = 3x^2 - 12xy + 7y^2.
I am unsure what diagonalization is in this context. I know what it means to diagonalize a matrix, say, A. You find it's eigenvectors, put them into a matrix, say S, find that matrix's inverse, and work out S^-1AS.
If someone could explain, that would be much appreciated.