What does the 'X' mean in the Mueller matrix rotation equation?

[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

 

[tiny-tim]

Welcome to PF!

Hi islahna! Welcome to PF!

… 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..

I don't know what that X is doing there …

in fact, I don't understand what that third line

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

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.

 

[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

 

[tiny-tim]

But I'm still curious, why they use that X sign, has got to be something ..mm.

Hi islahna!

dunno …

i don't have a copy of that book …

can you scan it?

 

[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

 

[tiny-tim]

I've contacted the author …

Well done!

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