Structure of the group preserving a bilinear form

TL;DR

This paper investigates the structure of the automorphism group of a vector space that preserves a given bilinear form, providing insights into its algebraic properties and classification.

Contribution

It offers a detailed analysis of the automorphism group preserving an arbitrary bilinear form, extending existing classifications to more general forms.

Findings

Characterization of the automorphism group structure

Classification results for different types of bilinear forms

Insights into symmetry properties of bilinear-preserving transformations

Abstract

We study the group of all linear automorphisms preserving an arbitrary bilinear form