Note: Richard Hill [rkhill@caci.com] provided the following info:
The definition of Stokes Vector components on (this) site is in error. Wolfram has it wrong also. The easiest way to see that it is wrong is to take horizontally polarized light (1, 1, 0, 0) and solve for the intensities. The total intensity I0 is ½ and the horizontal intensity I1 is 1. That obviously doesn't add. The Wikipedia explanation is consistent (Lord help us). S0 = I0 = I(horizontal) + I(vertical) S1 = I(horizontal)  I(vertical) = 2*I(horizontal)  I0 S2 = I(+45)  I(45) Please correct as desired.

Polarization  Stokes Vector 

Unpolarized  
Linear Horizontal  
Linear Vertical  
Linear +45°  
Linear 45°  
Circular, RightHanded  
Circular, LeftHanded 
Optical elements can be applied to Stokes vectors using Mueller matrices. The Stokes vector describes the polarization of a plane wave, and the Mueller matrix describes how the polarization changes upon scattering at a change in electrical or magnetic properties.
The Mueller Matrix contains everything optically one can obtain from a system of scatterers in a turbid medium. It is a matrix that can be used to reproduce the effect of a given optical element when applied to a Stokes vector.
Optical Element  Mueller Matrix 

Clear Filter  
Linear Horizontal Polarizer  
Linear Vertical Polarizer  
Linear Polarizer at +45°  
Linear Polarizer at 45°  
QuarterWave Plate, Fast Axis Vertical  
QuarterWave Plate, Fast Axis Horizontal  
Circular Polarizer, RightHanded  
Circular Polarizer, LeftHanded 

