vector spaces

Linear maps are functions between vector spaces that preserve vector addition and scalar multiplication.

A vector space is an algebraic structure consisting of a set of vectors together with a field of scalars, where vector addition and scalar multiplication satisfy specific axioms. It provides the foundation for linear algebra, including concepts such as subspaces, basis, dimension, and linear transformations.

Subspaces are subsets of a vector space that satisfy the vector space axioms under the same operations.