Singular case of pairs of bilinear, quadratic, or Hermitian forms

Abstract

The main object of this paper is a treatment of the equivalence of pairs of bilinear forms in the singular case by a purely rational method. The problem was first discussed by Kronecker,t who employed the irrational canonical form due to Weierstrass for the auxiliary non-singular case, instead of the rational canonical form (13) employed here. It is then a simple matter to deduce in Parts II and III the criteria for the equivalence of pairs of symmetric or Hermitian bilinear forms, or quadratic or Hermitian forms, in the singular case.