Vector space : A linear vector space is a set of objects that can be added and multiplied by a number with the result being again an object in the set. An example of a vector space is the set of two-dimensional vectors with componentwise addition and componentwise multiplication by a number. Another example is the linear vector space of continuous functions in which addition and multiplication with a number are defined on a point by point basis. The branch of mathematics that studies linear vector spaces is called linear algebra.