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Math Help - Mueller matrix - rotation

  1. #1
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    Mueller matrix - rotation

    Hi,
    I have a basic question on Mueller matrix which I came across upon reading through the Handbook of Optic, chapter 22 polarimetry. It says that :-

    -------
    when a polarization element with Mueller matrix M is rotated about the beam of light by an angle theta such that the angle of incident is unchanged, the resulting Mueller matrix M is :

    = M(theta)
    = R(theta) M R(-theta)
    = [matrix elements of R(theta)] [matrix elements of M] X [matrix elements of R(-theta)]
    ---------------

    My question is, what does the "X" mean here..

    Sorry if this is too basic, I've just started brushing up my matrix since college.

    Appreciate any help.

    regards,
    --islahna
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  2. #2
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    It appears to be just a multiplication sign. But it is peculiar that they would only use it in that one place.

    All this, [matrix elements of R(theta)] [matrix elements of M] X [matrix elements of R(-theta)], which I would think should be [matrix elements of R(theta)] X [matrix elements of M] X [matrix elements of R(-theta)] just means the same as the previous line: multiply those three matrices together.
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  3. #3
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    Multiply

    Its a multiplication sign. I've spend the last two years playing with those matrices.

    Mrot(theta)*M*Mrot(theta)
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  4. #4
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    hi HallsofIvy and Modilion,
    thank you so much for the insight. I'll take it as ordinary matrix mulitplication for now.
    But I'm still curious, why they use that X sign, has got to be something ..
    mm..will come back if i found something..

    thanks,
    --islahna
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  5. #5
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    Smile

    hi HallsofIvy and Modilion,

    I've contacted the author since and the following is the snippet from his response that I'd like to share.
    Hope it clarifies any doubts ..

    ------- start -------
    The x in Eq. 12 & 13 is just matrix multiplication and is there because the equation continued onto a second line. I understand how these little things can be so difficult to those starting who need the information the most.
    ------- end -----------

    thanks you.

    --islahna
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