About: Baker–Campbell–Hausdorff formula   Goto Sponge  NotDistinct  Permalink

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In mathematics, the Baker–Campbell–Hausdorff formula is the solution to the equation Z = log(eX eY) for possibly noncommutative X and Y in the Lie algebra of a Lie group. This formula tightly links Lie groups to Lie algebras by expressing the logarithm of the product of two Lie group elements as a Lie algebra element using only Lie algebraic operations. The solution on this form, whenever defined, means that multiplication in the group can be expressed entirely in Lie algebraic terms. The solution on another form is straightforward to obtain; one just substitutes the power series for exp and log in the equation and rearranges. The point is to express the solution in Lie algebraic terms. This occupied the time of several prominent mathematicians.

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  • Baker–Campbell–Hausdorff formula
  • Baker-Campbell-Hausdorff-Formel
  • Formula di Baker-Campbell-Hausdorff
  • Formule de Baker-Campbell-Hausdorff
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  • In der Mathematik ist die Baker-Campbell-Hausdorff-Formel eine nach den Mathematikern Henry Frederick Baker, John Edward Campbell und Felix Hausdorff benannte Gleichung, die ein Vertauschungsgesetz für bestimmte lineare Operatoren angibt.
  • En mathématiques, la formule de Baker-Campbell-Hausdorff est la solution de l'équation : où , et sont des matrices. Avec les crochets de Lie, elle s'écrit :
  • In mathematics, the Baker–Campbell–Hausdorff formula is the solution to the equation Z = log(eX eY) for possibly noncommutative X and Y in the Lie algebra of a Lie group. This formula tightly links Lie groups to Lie algebras by expressing the logarithm of the product of two Lie group elements as a Lie algebra element using only Lie algebraic operations. The solution on this form, whenever defined, means that multiplication in the group can be expressed entirely in Lie algebraic terms. The solution on another form is straightforward to obtain; one just substitutes the power series for exp and log in the equation and rearranges. The point is to express the solution in Lie algebraic terms. This occupied the time of several prominent mathematicians.
  • In matematica, la formula di Baker–Campbell–Hausdorff è la soluzione dell'equazione: per due grandezze X e Y noncommutanti (ad esempio matrici quadrate). Questa formula collega i gruppi di Lie con le algebre di Lie esprimendo il logaritmo del prodotto di due elementi del gruppo di Lie come un elemento dell'algebra di Lie in coordinate canoniche. La soluzione coinvolge le parentesi di Lie degli elementi X e Y; la sua scrittura, interrotta al terzo ordine, è: Questa formula prende il nome da Henry Frederick Baker, John Edward Campbell e Felix Hausdorff.
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