If (b₁,b₂,…,b_n) is a set of vectors forming a basis then an orthonormal basis (u₁,u₂,…,u_n) can be constructed by ${\tilde{u}}_j=b_j-{\displaystyle \sum _{k=1}^{j-1}\left(\frac{{\tilde{u}}_j^T{b}_k}{{\tilde{u}}_j^T{\tilde{u}}_j}\right)}{\tilde{u}}_j,u_j=\frac{{\tilde{u}}_j}{\left|{\tilde{u}}_j\right|}$