Least Squares Problems in Orthornormalization

Shanwen Hu

For any $n$-tuple $({\alpha }_1,...,{\alpha }_n)$ of linearly independent vectors in Hilbert space $H$, we construct a unique orthonormal basis $({\epsilon }_1,...,{\epsilon }_n)$ of $span\{{\alpha }_1,...,{\alpha }_n\}$ satisfying:…