Bases
Updated: October 29, 2020
a basis for an n-dimensional vector space \(V\) is any ordered set of linearly independent vectors \((\mathbf{e}_{1}, \mathbf{e}_{2},…,\mathbf{e}_{n})\)
An arbitrary vector \(\mathbf{x}\) in \(V\) can be expressed as a linear combination of the basis vectors:
\begin{equation} \mathbf{x}\,=\,\sum\limits_{i = 1}^{n} \mathbf{e}_{i}x^{i} \end{equation}