Vector Spaces: Concepts, History, and Applications Guide

Table of Contents A vector space is an additively written abelian group together with a field that operates on it. Vector spaces are often described as a set of arrows, i.e. a line segment with a direction that can be added, stretched, or compressed. That’s where the term linear to describe addition and operation, and the term scalar for the scaling factor from the operating field come from. Although there is basically no difference between the two definitions, the abstract definition is...