Holonomic modules have a tendency to behave like finite-dimensional vector spaces.

However, linear algebra is much simpler for finite-dimensional vector spaces.

This includes the classification of finite-dimensional vector spaces as a special case, where .

For every finite-dimensional vector space (viewed as a module over the base field), the length and the dimension coincide.

There is in general no natural isomorphism between a finite-dimensional vector space and its dual space.

In mathematical analysis, a domain is any connected open subset of a finite-dimensional vector space.

On a finite-dimensional vector space this topology is the same for all norms.

Let V be a finite-dimensional vector space with an ordered basis β.

Like any linear transformation of finite-dimensional vector spaces, a rotation can always be represented by a matrix.

Consider linear operators on a finite-dimensional vector space over a perfect field.