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Math Help - T-invariant subspace;inner product

  1. #1
    jax
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    T-invariant subspace;inner product

    In R^2 with the standard dot product, define T(x,y)=(2x+y,0). Find a subspace U of R^2 such that U is T-invariant but U orthogonal is not T-invariant. Does T fix all the vectors in the subspace U you found?

    I'm not really sure where to even start with this problem, any help would be appreciated!! thank you.
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  2. #2
    Senior Member roninpro's Avatar
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    You might note that you can generate a T-invariant subspace by taking a vector x\in V and taking the basis \{x, Tx, T^2x, T^3x,\ldots\}.
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