Abstract
In this chapter, we describe the foundations of the theory of non-degenerate symmetric bilinear forms on finite-dimensional vector spaces and their orthogonal groups. Among the highlights of this discussion are the Cartan–Dieudonne Theorem, which states that any orthogonal transformation is a finite product of reflections, and Witt’s Theorem giving a partial normal form for quadratic forms. The theory of split symmetric bilinear forms is found to have many parallels to the theory of symplectic forms, and we will give a discussion of the Lagrangian Grassmannian in this spirit.
Full Text
Published Version
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call