What is the definition of a vector space?

A vector space is defined as a set of vectors that can be added together and multiplied by scalars, with these operations satisfying specific axioms. The key features of a vector space include the ability to perform vector addition and scalar multiplication while adhering to several axioms, such as closure, associativity, commutativity of addition, existence of a zero vector, and the existence of additive inverses.

This definition encompasses both the operations involved and the properties that must be upheld, thus establishing a structured and consistent framework for working with vectors. The inclusion of specific axioms is crucial as these conditions ensure that the vectors behave in a predictable manner within the space, allowing for the development of further linear algebra concepts and operations.