Classification of linear mappings between indefinite inner product spaces

Abstract

Let A:U→V be a linear mapping between vector spaces U and V over a field or skew field F with symmetric, or skew-symmetric, or Hermitian forms B:U×U→F and C:V×V→F.We classify the triples (A,B,C) if F is R, or C, or the skew field of quaternions H. We also classify the triples (A,B,C) up to classification of symmetric forms and Hermitian forms if the characteristic of F is not 2.