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    Let T be an element of L ( complex numbers^3 ) and suppose 0 is the only eigenvalue for T. Show that T^n = 0 for some n.

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    Let T be an element of L ( complex numbers^3 ) and suppose 0 is the only eigenvalue for T. Show that T^n = 0 for some n.

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    https://brainmass.com/math/linear-algebra/element-complex-numbers-217198

    Solution Preview

    Proof:
    We consider the characteristic function of T: f(x) = det(xI - T). We know that f(x) is a polynomial with degree 3 because T is an ...

    Solution Summary

    A proof involving complex numbers, eigenvalues and determinants is provided.

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