Explore BrainMass
Share

Explore BrainMass

    Minimal polynomial and stabilizer

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    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....

    © BrainMass Inc. brainmass.com October 9, 2019, 9:05 pm ad1c9bdddf
    https://brainmass.com/math/linear-transformation/minimal-polynomial-stabilizer-172613

    Attachments

    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.

    $2.19