ABSTRACT
O(N) group The N-dimensional orthogonal group. This group is the rotation group in N dimensions. A point in N dimensions is given by N numbers, xi (where i=1, . . . , N). The O(N) group transforms xi to x′i (xi = Oijx′j ) in such a way that xi ·xi =x′i ·x′i (i.e., the N-dimensional length remains invariant). O(N) has 12N(N −1) independent generators.
