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Math Help - Diagonalization

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    Diagonalization

    Let T be a linear operator on the n-dimensional vector space V, and suppose that T has n distinct characteristic values. Prove that T is diagonalizable
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    Quote Originally Posted by Chandru1 View Post
    Let T be a linear operator on the n-dimensional vector space V, and suppose that T has n distinct characteristic values. Prove that T is diagonalizable
    T is diagonalisable if V has a basis consisting of eigenvectors of T. But eigenvectors associated with distinct eigenvalues are linearly independent. If all n eigenvalues are distinct then there must be n linearly independent eigenvectors, and they form a basis.
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