> [!NOTE] Definition > Let $V$ be a [[Finite Dimensional Real Vector Space|finite dimensional real vector space]]. The **dimension** of $V$ is given by the [[Cardinality|cardinality]] of any [[Basis of a Real Vector Space|basis]] of $V,$ denoted $\dim V$ or $\dim_{\mathbb{R}} V,$ when it is useful to emphasise that the scalars are $R$. **Note**: By [[Cardinality of Any Two Bases of Finite Dimensional Real Vector Space are Equal (Dimension of FDVS is well-defined)]], $\dim V\in \mathbb{N}$ is well-defined.