Editing Complexification (section)

{{Short description|Topic in mathematics}}
{{for|the complexification of a real Lie group|Complexification (Lie group)}}
In [[mathematics]], the '''complexification''' of a [[vector space]] {{math|''V''}} over the field of real numbers (a "real vector space") yields a vector space {{math|''V''{{i sup|'''C'''}}}} over the [[complex number]] [[field (mathematics)|field]], obtained by formally extending the scaling of vectors by real numbers to include their scaling ("multiplication") by complex numbers. Any [[Basis (linear algebra)|basis]] for {{math|''V''}} (a space over the real numbers) may also serve as a basis for {{math|''V''{{i sup|'''C'''}}}} over the complex numbers.