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Math Help - Finding unknown matrix

  1. #1
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    Finding unknown matrix

    Hello guys,

    I am having problem in finding an unknown matrix from matrix multiplication

    Right now I am at this point

    X . Y = Y . Z

    Where X,Y and Z are 2x2 matrices. Among these X and Z are known and I have to compute Y.
    I am trying to solve it by element by element multiplication, supposing Y = [y11 y12;y21 y22]

    Can anyone tell me exact method or alternate equality of this relation what I mentioned above?

    Thanks
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  2. #2
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    Re: Finding unknown matrix

    As I understand you, you don't know anything about the entries in X Y or Z? Are you given any further information?

    If Y is invertible, then you can right-multiply each side by the inverse of Y and then X will be similar to Z.

    One solution: if Y is the zero matrix, the equation will always be true. If X = Z, then Y is the identity matrix, or some other matrix with which X commutes. The most general rule I know of is that two matrices will commute iff they are both diagonalizable to the same basis. Some 2x2 matrices, of course, are not diagonalizable at all.
    Last edited by zhandele; December 3rd 2012 at 07:30 PM. Reason: afterthought
    Thanks from topsquark
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  3. #3
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    Re: Finding unknown matrix

    Firstly thanks for considering my querey =)

    I know about enteries of X and Z and they are not equal. All (X,Y and Z) follows properties of ABCD Chain matrix.

    By knowing X and Z, I reached at point where all elements of Y are giving result 0. It shouldn't be so...
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  4. #4
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    Re: Finding unknown matrix

    - a*((323*b)/(10000*(a*d - b*c)) - (33*d)/(250*(a*d - b*c))) - c*((173*b)/(5000*(a*d - b*c)) - (71*d)/(500*(a*d - b*c))) = 0.1324

    - b*((323*b)/(10000*(a*d - b*c)) - (33*d)/(250*(a*d - b*c))) - d*((173*b)/(5000*(a*d - b*c)) - (71*d)/(500*(a*d - b*c))) = 0.0298

    a*((323*a)/(10000*(a*d - b*c)) - (33*c)/(250*(a*d - b*c))) + c*((173*a)/(5000*(a*d - b*c)) - (71*c)/(500*(a*d - b*c))) = 0.1526

    b*((323*a)/(10000*(a*d - b*c)) - (33*c)/(250*(a*d - b*c))) + d*((173*a)/(5000*(a*d - b*c)) - (71*c)/(500*(a*d - b*c))) = 0.0342

    Here is matlab computed result. Where a,b,c and d are y11,y12,y21 and y22 respectively.
    Result suppose to be a = 0.9, b=0.10, c=0.11 and d=0.12, but i couldn't reach at this point
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