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Math Help - Inner product space

  1. #1
    MHF Contributor Also sprach Zarathustra's Avatar
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    Inner product space

    Let V be inner product space with dim(V)<inf.
    Let T:V-->V be a linear transformation. Prove:

    1. (ImT)^# = kerT*

    2. (kerT)^# = imT*

    (*=unitary operator )
    (#=orthogonal complement )
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  2. #2
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    Quote Originally Posted by Also sprach Zarathustra View Post
    Let V be inner product space with dim(V)<inf.
    Let T:V-->V be a linear transformation. Prove:

    1. (ImT)^# = kerT*

    2. (kerT)^# = imT*

    (*=unitary operator )
    (#=orthogonal complement )

    Your last three questions are standard stuff. You can find it in any decent linear algebra book. Check, for example, the book "Algebra" by Prof. S. Amitzur, or the one by Prof. Levi, both in hebrew, Ed. Akademon , The Hebrew University.
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