Reduce the quadratic form $q(x,y) = 6xy$ using the orthogonal reduction (i.e, find a orthogonal basis such that the matrix of the bilinear form is diagonal and $a_{ii} = 0$ or $a_{ii} = ^+_-1$)
What is exactly the process of "orthogonal reduction"? I mean, to find this basis, Which vector should I use to start my orthogonal basis? If I take $(0,1)$, for example, then $q(0,1) = 0$. Should I ever start with the canonic basis of $R^2$ if it doesnt say anything (should I admit using the canonic base)?
thanks in advance!