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Math Help - Verify d/dx linear tranformation

  1. #1
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    Verify d/dx linear tranformation

    How do I verify that the operations d/dx and d^2/dx^2 act as a linear transformations on the space C^1?
    Last edited by thehollow89; March 21st 2009 at 08:00 PM.
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    Quote Originally Posted by thehollow89 View Post
    How do I verify that the operations d/dx and d^2/dx^2 act as a linear transformations on the space C^1?
    Notice that \mathcal{L}(cf) = c\mathcal{L}(f) and \mathcal{L}(f+g) = \mathcal{L}(f) + \mathcal{L}(g) where \mathcal{L} is \tfrac{d}{dx} or \tfrac{d^2}{dx^2} if we want to abuse notation.
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