Inner-Product Spaces, Euclidean Spaces

Abstract

As in Chap.2, the term “linear space” will be used as a shorthand for “finite dimensional linear space over ℝ”. However, the definitions of an inner-product space and a Euclidean space do not really require finite-dimensionality. Many of the results, for example the Inner-Product Inequality and the Theorem on Subadditivity of Magnitude, remain valid for infinite-dimensional spaces. Other results extend to infinite-dimensional spaces after suitable modification.