Vector spaces

the basic algebraic structure of linear algebra; a module over a field, such that its elements can be added together or scaled by elements of the field

number of vectors in any basis of the vector space

vector space equipped with a compatible topology

function whose range is a subset of the real numbers

In mathematics, the complexification of a vector space over the field of real numbers (a "real vector space") yields a vector space over the complex number field, obtained by formally extending the scaling of vectors by real numbers to include their scaling ("multiplication") by complex numbers. Any basis for (a space over the real numbers) may also serve as a basis for over the complex numbers.

algebraic structure that is easily decomposable into subspaces

vector space with a partial order