Vector spaces

A vector space is a collection of objects called vectors that can be added together and multiplied by numbers (scalars), such as real numbers, while still remaining within the collection. These operations follow specific rules, like combining vectors to get another vector and scaling vectors proportionally. Vector spaces are fundamental in mathematics for modeling many systems, from physics to computer science, because they provide a structured way to analyze and manipulate quantities that have direction and magnitude, or more abstract versions of these concepts.