Mueller matrix - rotation

1. Jan 5, 2009

islahna

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..
From my reading, the cross product is used with vector. This time, it's a matrix.

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

Appreciate any help.

regards,
--islahna

2. Jan 6, 2009

tiny-tim

Welcome to PF!

Hi islahna! Welcome to PF!
I don't know what that X is doing there …

in fact, I don't understand what that third line
is supposed to mean at all.

The first and second lines, effectively M' = RMR-1, are just the standard formula for the effect of rotation R on matrix M …

it's ordinary matrix mulitplication.

3. Jan 8, 2009

islahna

hi tiny-tim,
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.

thanks,
--islahna

4. Jan 9, 2009

tiny-tim

Hi islahna!

dunno

i don't have a copy of that book …

can you scan it?

5. Jan 11, 2009

islahna

hi tiny-tim,

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

6. Jan 12, 2009

tiny-tim

Well done!!

Duh … an author trying to avoid one source of confusion by creating another one!