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Math Help - inner product space question

  1. #1
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    inner product space question

    I have a question.
    If T is a linear operator on an inner product space, say V, and W is a T-invariant subspace of V, how could I show that W^{\perp} is T*-invariant, where T* is the adjoint of T.
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  2. #2
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    Quote Originally Posted by dannyboycurtis View Post
    I have a question.
    If T is a linear operator on an inner product space, say V, and W is a T-invariant subspace of V, how could I show that W^{\perp} is T*-invariant, where T* is the adjoint of T.

    For w'\in W^\perp we get:

    T^{*}w'\in W^\perp\Longleftrightarrow <w,T^{*}w'>=0\,\,\,\forall w\in W\Longleftrightarrow <Tw,w'>=0\,\,\,\forall w\in W...but this last equality is true....

    Tonio
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