A _Hausdorff pre-Hilbert Space_ or simply a _pre-Hilbert space_ is any [vector space](Vector%20spaces.md) ([real](Real%20vector%20spaces.md) or [complex](Complex%20vector%20spaces.md)) that is equipped with an [inner product](Inner%20products.md). Thus,  #MathematicalFoundations/Algebra/AbstractAlgebra/LinearAlgebra/VectorSpaces