# Thread: Mueller matrix - rotation

1. ## 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)]
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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

2. 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.

3. ## Multiply

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

Mrot(theta)*M*Mrot(theta)

4. 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

5. 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