Dimension of a Subspace

Let $V$ be a subspace of ${\mathbb{R}}^n$.

The dimension of $V$, written as $\dim V$ is the size (number of vectors) in the set of vectors defining the basis of $V$.

Example

The standard basis of ${\mathbb{R}}^n$ has $n$ vectors, and thus we write:

$$\dim {\mathbb{R}}^n=n$$

Related

• Rank of a Matrix
• Column Space of a Matrix