A vector space is a mathematical concept that refers to a collection of objects called vectors that can be added and multiplied by numbers called scalars. There are several synonyms for vector space, including linear space, linear manifold, and linear subspace. These terms are often used interchangeably with vector space but can refer to slightly different variations of the concept. For example, a linear subspace is a subset of a vector space that retains the essential properties of a vector space, while a linear manifold is a more general concept that refers to a space that can be locally approximated by a linear space. Ultimately, all of these synonyms describe the same fundamental mathematical concept that is essential to fields such as linear algebra and physics.