Classification of sesquilinear forms with the first argument on a subspace or a factor space Original Research Article

Let V be a vector space over a field or skew field image, and let U be its subspace. We study the canonical form problem for bilinear or sesquilinear formsimageand linear mappings U → V, V → U, V/U → V, V → V/U. We solve it over image and reduce it over all image to the canonical form problem for ordinary linear mappings W → W and bilinear or sesquilinear forms image. Moreover, we give an algorithm that realizes this reduction. The algorithm uses only unitary transformations if image, which improves its numerical stability. For linear mapping this algorithm can be derived from the algorithm by Nazarova et al. [L.A. Nazarova, A.V. Roiter, V.V. Sergeichuk, V.M. Bondarenko, Application of modules over a dyad for the classification of finite p-groups possessing an abelian subgroup of index p and of pairs of mutually annihilating operators, Zap. Nauchn. Sem., Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 28 (1972) 69–92, translation in J. Soviet Math. 3 (5) (1975) 636–654].