7 - Bilinear Forms and Quadratic Forms

Abstract

This chapter discusses a useful way to classify quadratic forms and describes methods for simplifying them. It also discusses the bilinear forms. A bilinear form on a vector space V is a bilinear mapping V × V → F, where F is the field of scalars. The chapter describes the characteristic values of a real symmetric matrix as extrema of suitably defined functions. It also explains a rule called Lagrange's method of undetermined multiples, which finds out the stationary points a function whose variables are constrained by a side condition.