Bilinear Forms

Total 4 Posts

Introduction to Quadratic Forms

This tutorial introduces the quadratic forms associated with symmetric bilinear forms.

Orthogonal Decompositions

In this tutorial we learn that over an arbitrary field, every finite-dimensional bilinear space has an orthogonal decomposition into subspaces of dimension at most two. Over a field of characteristic not two, every finite-dimensional bilinear space possesses an orthogonal basis.

Bilinear Forms over Free Modules

This tutorial explains the connection between bilinear forms over free modules and Gram matrices.

Introduction to Bilinear Forms

Before embarking on a journey to study quadratic (and hermitian) forms on modules over general rings, we will learn about bilinear forms over rings