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Are you able to solve this Simple Matrix Challenge?

  1. Jun 28, 2009 #1
    I am working with 2 by 2 matrices, L, X, P and T.

    L = PTP -------Eqn 1
    X = PTTTTTTP ----------Eqn 2

    where L and X are known matrices. P and T matrix are unknown and are to be solved.

    The above problem looks simple but are you able to solve it?
  2. jcsd
  3. Jun 28, 2009 #2
    Can you do a simple special case? for example

    L = \left[1, 0; 0, 1\right], X = \left[0, 1; 0, 0\right]
  4. Jun 28, 2009 #3
    Let's use some numbers as an illustration.
    For example,
    P = [1 1;1 1]; T = [ 1 2;3 4 ];
    L = P*T*P = [10 10;10 10];
    X = P*T*T*T*T*T*T*P = [44966 44966;44966 44966];

    We only have L and X. The problem is how to get back P and T.
  5. Jun 29, 2009 #4
    it seems to be solving some linearlity problem,
    however this question can lead to ambiguos solutions,
    i assume your question is bound to only by setting the P to be [1,1;1,1],
    otherwise this question is meaningless.

    i don't know, perhaps i'm wrong? why don't you propose your solution since you're confident and done some research?
  6. Jun 29, 2009 #5


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    If it were L= PTP-1, the problem would be simple. But with L= PTP, ...
  7. Jun 29, 2009 #6
    and i doubted that if the elements within changed,
    would it still be "simple" ?

    for e.g, complex element, exponential, differential variable?

    And it definitely not 'simple' as it looks,
    from the first view it is already harzardous.
  8. Jun 29, 2009 #7
    I am sorry to tell you that your problem is under defined. Even if we assume all matrices to be invertible you will get the same equations if you substitute P for -P.
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