Classification problems for system of forms and linear mappings

Abstract

We devise a method that reduces the problem of classifying systems of forms and linear mappings to the problem of classifying systems of linear mappings. Canonical matrices of (i) bilinear or sesquilinear forms, (ii) pairs of symmetric, skew-symmetric, or Hermitian forms, (iii) isometric or selfadjoint operators on a space with nonsingular symmetric, or skew-symmetric, or Hermitian form are obtained over any field of characteristic not 2 up to classification of Hermitian forms over its finite extensions.

46 pages

Cited by in corpus (6)

• Canonical matrices of bilinear and sesquilinear forms
• A regularization algorithm for matrices of bilinear and sesquilinear forms
• Canonical matrices of isometric operators on indefinite inner product spaces
• Congruence of multilinear forms
• Tridiagonal canonical matrices of bilinear or sesquilinear forms and of pairs of symmetric, skew-symmetric, or Hermitian forms
• Classification of sesquilinear forms with the first argument on a subspace or a factor space