Editing Exponential function (section)

==Lie algebras==
Given a [[Lie group]] {{math|''G''}} and its associated [[Lie algebra]] <math>\mathfrak{g}</math>, the [[exponential map (Lie theory)|exponential map]] is a map <math>\mathfrak{g}</math> {{math|↦ ''G''}} satisfying similar properties. In fact, since {{math|'''R'''}} is the Lie algebra of the Lie group of all positive real numbers under multiplication, the ordinary exponential function for real arguments is a special case of the Lie algebra situation. Similarly, since the Lie group {{math|GL(''n'','''R''')}} of invertible {{math|''n'' × ''n''}} matrices has as Lie algebra {{math|M(''n'','''R''')}}, the space of all {{math|''n'' × ''n''}} matrices, the exponential function for square matrices is a special case of the Lie algebra exponential map.

The identity <math>\exp(x+y)=\exp(x)\exp(y)</math> can fail for Lie algebra elements {{math|''x''}} and {{math|''y''}} that do not commute; the [[Baker–Campbell–Hausdorff formula]] supplies the necessary correction terms.