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    Determine the Eigenvalues of a Function

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    K is a field, V is the vector space of all polynomials over K, D is the derivative function from V to V and g is a linear function from V to V given by

    g(f(x)) = xDf(x).

    Find all eigenvalues of g. When are there infinitely many eigenvalues? Please explain in detail.

    PLEASE NOTE: it states that g is a linear function from V to V. This means f lies in the domain of g i.e f lies in V. Therefore f is a polynomial and cannot be the exponential function

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    Solution Summary

    Eigenvalues are found. The solution is detailed and well presented. The response received a rating of "5" from the student who posted the question.