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Math Help - Matrix power proof help.

  1. #1
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    Matrix power proof help.

    I was shown a 2x2 matrix power formula, given here:

    An=(λ21n12n)/(λ21)*I + (λ2n1n)/(λ21)*A

    And I found that I quite liked it. I brought it up to my professor, and asked if something like this could be used on an exam, and he said that it could, if I could prove it. I can see that it likely has it's roots in the Cayley-Hamilton theorem, but I am curious as to how the two coefficients were worked out. I originally tried to solve it with the A=PDP-1 method, but quickly found myself drowning in long equations, and my abcd matrix was being represented with just a and b, leaving no c and d. (and thereby making it difficult/impossible to extract the A matrix)

    Can anyone give me a hint? Thank you.
    Last edited by Latsabb; April 16th 2014 at 06:08 AM.
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  2. #2
    MHF Contributor
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    Re: Matrix power proof help.

    JohnG has posted the exact proof you are after here.
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  3. #3
    Junior Member
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    Re: Matrix power proof help.

    Perfect! Thank you very much.
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