Math — Gram–Schmidt Process

\mathbf{u}_1 = \mathbf{v}_1

\mathbf{u}_k = \mathbf{v}_k - \sum_{j<k}\frac{\langle \mathbf{v}_k,\mathbf{u}_j\rangle}{\langle \mathbf{u}_j,\mathbf{u}_j\rangle}\mathbf{u}_j

\mathbf{e}_k = \frac{\mathbf{u}_k}{\|\mathbf{u}_k\|}

\Rightarrow \text{orthonormal basis}