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Math Help - Linear Operator

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    Linear Operator

    Let T be a linear operator on an n-dimensional space and suppose that T has n distinct characteristics values. Prove that any linear operator which commutes with T is a polynomial in T.
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    Re: Linear Operator

    Quote Originally Posted by problem View Post
    Let T be a linear operator on an n-dimensional space and suppose that T has n distinct characteristics values. Prove that any linear operator which commutes with T is a polynomial in T.
    Start with the fact that T has n distinct characteristics values. What can you say about such an operator (think in terms of matrices)? What can you say about the matrix of an operator that commutes with T?
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