This is perhaps the best "default definition".
- All indefinite orthogonal groups of matrices of equal metric signature are isomorphic | 179
- Definition of the indefinite orthogonal group | 204, 383, 1
- The orthogonal group is the group of all invertible matrices where the inverse is equal to the transpose | 102
- The orthogonal group is the group of all matrices with orthonormal rows and orthonormal columns | 37
- What happens to the definition of the orthogonal group if we choose other types of symmetric bilinear forms | 172