Background

Abstract

We begin by reviewing some of the fundamental algebraic, geometric and analytic ideas we use throughout the book. Our setting, for most of the book, is an arbitrary Euclidean space E, by which we mean a finite-dimensional vector space over the reals R, equipped with an inner product 〈.,.〉. We would lose no generality if we considered only the space Rⁿ of real (column) n-vectors (with its standard inner product), but a more abstract, coordinate-free notation is often more flexible and elegant.