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Math Help - A Linear Transformation question

  1. #1
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    A Linear Transformation question

    give an example of a linear transformation  \, T:R^2 \rightarrow R^2 where T^2=T and 0,1 are the eigenvalues.

    Attempt:
    <br />
T(x,y) = (x,0)

    *T(T(x,y) = T(x,0) = (x,0)
    *T(x,y) = (x,0)

    T(1,0) = (1,0) = 1(1,0)
    T(0,1) = (0,0) = 0(0,1)

    Is this correct?

    Thanks!
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  2. #2
    MHF Contributor

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    Yes, that's exactly right! Any linear transformation that satifies " T= T^2" is a "projection" onto some subspace. Here, you chose to project onto the x-axis.

    Any one dimensional subspace of R^2 is a line through the origin, (x, y)= (x, ax) for some number a (or the y-axis, (0, y)). It's not easy but you might try to find the projection that maps (x_0, y_0) onto that line.
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