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Math Help - Is it possible to solve a system of equations with unknown matrices?

  1. #1
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    Is it possible to solve a system of equations with unknown matrices?

    So I have a series of experimentally determined 2x2 matrices (y0, y1, y2...) and I know each of them is a product of two 2x2 matrices (a, b, and c). Ultimately I have three unknown matrices and six equations as follows:


    [y0] = [a][b]
    [y1] = [b][a]
    [y2] = [a][c]
    [y3] = [c][a]
    [y4] = [b][c]
    [y5] = [c][b]

    These matrices will not always be diagonalizable but sometimes they are (in which case its not a problem).
    I have found a solution to get an equation with one of the unknown matrices squared (ex: [y0][y5]^-1[y3] = [a][a]) but I'm not sure if the square root will always work.
    If you take the numbers out of the matrices it seems like there should be 24 eqautions (6*4) but only 12 unknowns (3*4) but that may be not true because they aren't linear.
    Thanks!
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  2. #2
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    Re: Is it possible to solve a system of equations with unknown matrices?

    Hey jlawrence6809.

    Even if you have a non-linear system to solve, you should still be able to solve the system using numerical techniques. Is this something you have tried?
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  3. #3
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    Re: Is it possible to solve a system of equations with unknown matrices?

    It took me a few days to do this but I was able to solve it non-linearly! If someone in the future needs the matlab code just pm me and I should get an email. Thanks!
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