Finite dimensional Hilbert space While Hilbert spaces originally refer to infinite dimensional complete inner product spaces they, by definition, include finite dimensional complete inner product spaces as well. In physics, they are often referred to as finite dimensional Hilbert spaces. For every finite dimensional Hilbert space there exist orthonormal basis kets that span the entire Hilbert space.
finite dimensional hilbert space while hilbert spaces originally refer to infinite dimensional complete inner product spaces they by definition include finite dimensional complete inner product spaces as well in physics they are often referred to as finite dimensional hilbert spaces for every finite dimensional hilbert space there exist orthonormal basis kets that span the entire hilbert space