Dual Vector Spaces and Multilinear Algebra

Abstract

This chapter begins with two sections on some important constructions on vector spaces, leading to quotient spaces and dual spaces. The section on dual spaces is based on the concept of a bilinear form defined on a pair of vector spaces. The next section contains the construction of the tensor product of two vector spaces and provides an introduction to the subject of what is called multilinear algebra. The last section contains an application of the theory of dual vector spaces to the proof of the elementary divisor theorem, which was stated in Section 25.