7.1. Introduction to Vector Spaces

This chapter will bring together much of what has been covered in previous subsections to add greater depth to our understanding of -dimensional space and its associated objects and operations. It is easiest to understand vector spaces by first considering what is known as the span of a set of vectors. As an example, we will start with the following vector set.  The span of a vector set is the subspace composed of all the possible linear combinations of the vectors in that set. Formally, this can be written as follows: