Definition:Dimension of Vector Space/Finite

Definition
Let $V$ be a vector space which is $n$-dimensional for some $n \in \N_{>0}$.

Then $V$ is finite dimensional.

The dimension of a finite-dimensional $K$-vector space $V$ is denoted $\map {\dim_K} V$, or just $\map \dim V$.

Also known as
Some sources use a hyphen, thus referring to a finite-dimensional vector space.

Also see

 * Bases of Finitely Generated Vector Space have Equal Cardinality