# Hilbert Space

### From Conservapedia

**Hilbert space** is an inner product space that is also a complete metric space. A Hilbert space is always a Banach space, but the converse need not hold. Hilbert space is named after mathematician David Hilbert, who used it to provide a natural context in which to generalize the concept of Fourier series and Fourier transformation in terms of arbitrary orthogonal functions defined on infinite dimensional inner product space.