ABSTRACT
We have introduced the isometry group of a bilinear space in §7.1 and separated the isometry groups of symmetric and alternating spaces. Here we begin by showing how to realize the isometry group as a group of nonsingu- lar matrices and then we prove a version of the Cartan-Dieudonné’s theorem on generation of the orthogonal group by symmetries. We also determine the center of orthogonal group. Section 10.3 gives a parallel treatment of the symplectic group.
