You need n vectors in the basis set of Rn

• The proof in reference is pretty weird.

• Since the set of ${\vec{e}}_i$ vectors is a basis for $R^n$, every vector in $R^n$ can be represented as a linear combination of ${\vec{e}}_i$.

• To represent each component of a vector in $R^n$, we’ll need $n{\vec{e}}_i$ vectors as each can represent only one component.

• Hence $k=n\square$.