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Math Help - calculation of lie brackets

  1. #1
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    calculation of lie brackets

    Hello!

    We have two vectorfields on \mathbb{R}^n X(x)=Ax+a, Y(x)=Bx+b, where A,B are nxn-matrices and a, b \in \mathbb{R}^n.

    Is it true that the lie bracket [X,Y]=0?
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  2. #2
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    What happens when you plug your vector fields into the definition of the Lie bracket?
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  3. #3
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    Thanks for your answer. Thats what i did. I just want to be sure if my calculation is right. The lie bracket of X and Y is zero since the Hessian Matrix of a smooth function is symmetric.

    Is the result correct?
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