= Hilbert Space = A '''Hilbert space''' is a generalized [[LinearAlgebra/InnerProduct|inner product space]]. <> ---- == Description == Recall that an [[LinearAlgebra/InnerProduct|inner product space]] is any [[LinearAlgebra/Linearity|linear space]] for which an inner product can be defined. Hilbert spaces are the completion of inner product spaces. That is, while inner product spaces have a finite number of dimensions, Hilbert spaces can be infinitely dimensional. They can also be real or complex valued. ---- CategoryRicottone