Dimension

The dimension of a vector space \(V\) is the number of linearly independent vectors that span \(V\), i.e. the minimum number \(d\) such that any element in \(\mathbf{v}\in V\) can be represented as \(\mathbf{v}=\sum_{i=1}^d \alpha_i \mathbf{b}_i\). The vectors \(\{\mathbf{b}_i\}_{i=1}^d\) are called a basis for \(V\), which are not unique in general.