I would like to find the (linear) involutions that conserve the quadratic form $x^2+y^2-z^2$.
Finding reasonable equations for the entries of the matrix is possible, but not particularly nice or enlightening. Alternatively, I could start with the fact that involutions are similar to one of four matrices, but I could not use that to find a satisfying description, either.
I would be happy both with a full answer or advice on what kind of description I could reasonably expect.