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    Minimal polynomial and stabilizer

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    Any explanations of the attached definitions is greatly appreciated. Thank you.

    The definition of the minimal polynomial for the linear transformation....
    the relationship between the cosets in G of the stabilizer....

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    Solution Preview

    Please see the attachment.

    (a) For linear transformation , we define

    Then the minimal polynomial of is the monic polynomial which generates .
    In another word, the minimal polynomial is the monic polynomial at the least
    degree in .
    For example, maps from to . ...

    Solution Summary

    This explains the definition of a minimal polynomial for a linear transformation and the relationship between cosets in the stabilizer.