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Thread: Help with Matrix Limits

  1. #1
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    Help with Matrix Limits

    I suck at these, especially in the complex field. This one's thankfully a real one but I'm having some trouble.

    Let A, B be 2x2 matrices with real entries st lim A^m, lim B^m, and lim (AB)^m exist as m --> inf, but Lim (AB)^m != (lim A^m)(lim B^m). Find A & B.

    I'm assuming there's no one correct answer.
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Re: Help with Matrix Limits

    Quote Originally Posted by lutheranian View Post
    I suck at these, especially in the complex field. This one's thankfully a real one but I'm having some trouble.

    Let A, B be 2x2 matrices with real entries st lim A^m, lim B^m, and lim (AB)^m exist as m --> inf, but Lim (AB)^m != (lim A^m)(lim B^m). Find A & B.

    I'm assuming there's no one correct answer.
    Well, what have you tried? This is obviously true if $\displaystyle A,B$ commute, so have you tried some natural examples?
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