Vector spaces

Abstract

In the previous chapter we reviewed the basic notions of vectors in space and their elementary application to the study of lines and planes. We derived elementary vector equations for lines and planes and saw how once a coordinate system was chosen these vector equations lead to the familiar equations of analytic geometry. However, particularly in application to physics, it is often very important to know the relation between the equations for the same plane (or line) in different coordinate systems. This leads us to the notion of a coordinate transformation. The appropriate domain in which to study such transformations is the abstract vector spaces to be introduced now.