Metric preserving group

1. Mar 29, 2010

Andy32

1. The problem statement, all variables and given/known data
Show that the real linear transformations of Rn preserving a real symmetric metric  form
a matrix Lie group, and that the group is determined up to isomorphism by the number
p of positive eigenvalues of , the number q of negative eigenvalues of , and the number
r of zero eigenvalues of , with p + q + r = n.

Does anybody know how to do this? Thanks
2. Relevant equations

3. The attempt at a solution