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

TL;DR

This paper provides canonical matrix representations for sesquilinear forms involving a subspace or factor space of a complex vector space, aiding in their classification and analysis.

Contribution

It introduces canonical matrices for sesquilinear forms with arguments on subspaces or factor spaces, extending the classification framework.

Findings

Canonical matrices for sesquilinear forms involving subspaces.

Explicit forms for forms with arguments on factor spaces.

Enhanced understanding of sesquilinear form classification.

Abstract

We give canonical matrices of bilinear or sesquilinear forms UxV-->C, (V/U)xV-->C, in which V is a vector space over the field C of complex numbers and U is its subspace.