Analytic Geometry of Euclidean Spaces

Abstract

We begin by describing some geometrical concepts. This approach may seem strange in a book on algebra, but the influence of geometry is fundamental to our subject, since the underlying geometrical ideas provide motivation, examples, and applications for the algebraic constructions. In fact, the adjective “linear” in this book’s title means “pertaining to lines” (which in mathematics usually mean straight lines), and indicates the geometric origins of linear algebra.

The original version of this chapter was revised. An erratum can be found at https://doi.org/10.1007/978-0-8176-8325-2_9