Classical group

Summary

The classical groups are the general linear groups and special linear groups, and the groups of linear maps that preserve a nondegenerate form. For symmetric, alternating and Hermitian forms these are the orthogonal, symplectic and unitary groups. The name goes back to Hermann Weyl's book on the classical groups. Over $\C$ they give all the complex simple Lie groups except five exceptional ones, up to local isomorphism. Over finite fields, their projective versions give several infinite families of finite simple groups.