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Math Help - Upper Triangular Matrix

  1. #1
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    Upper Triangular Matrix

    Hi I've got this question on an upcoming assignment and I can't think what to do except I think V can't be complex.

    Give an example of a vector space V and a linear transformation T such that T cannot be represented by an upper triangular matrix with respect to any basis of V

    Any help would be great
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  2. #2
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
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    Are you familiar with Schur's theorem? A real matrix has a Schur decomposition iff all of its eigenvalues are real. So its characteristic polynomial must split.
    I hope this helps.

    You are correct that every complex matrix has a Schur decomposition
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