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Math Help - Linear Transformation and Matrices #2.

  1. #1
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    Linear Transformation and Matrices #2.

    Let V be the vector space of real-valued continuous functions with ordered bases S={sin t, cos t} and consider T={sin t - cos t, sin t + cos t}, another ordered basis for V. Find the representation of the linear operator L: V --> V defined by L(f) = f' with respect to:
    (a) S
    (b) T
    (c) S and T
    (d) T and S
    Last edited by mr fantastic; April 16th 2011 at 05:59 PM. Reason: Title.
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  2. #2
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    again, what you want to do is examine what L does to the elements of S, or T.

    the whole point of a basis, is that every element in V is a linear combination of basis elements. and L is a linear map, so determining L's action on basis elements determines L completely.
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