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 :-

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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

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.

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

Mrot(theta)*M*Mrot(theta)

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

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