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Math Help - Matrix operation

  1. #1
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    Matrix operation



    Determine A^18

    dont know what to do besides to just count. But i had a similar question before where i could se it was a rotation matrix and then it was easy. Is there an easy way for this one to?

    Thanks!
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Decompose



    and apply the Newton's binomial theorem. The matrix N is nilpotent of order 3.
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  3. #3
    A Plied Mathematician
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    Two comments:

    1. Your matrix is in Jordan Normal Form already.
    2. Take a look here.

    Cheers.
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  4. #4
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    Jordan Normal Form did the job really easy

    Cheers!
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  5. #5
    A Plied Mathematician
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    I think FernandoRevilla's method and my proposed method boil down to the same thing (as they should!). The binomial theorem is going to give you those binomial coefficients that are showing up in the Jordan Normal Form power section of the wiki post.
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