The description of stokes parameter is an excellent attempts to provide a smplified and understandable explaination of this abstract matrix. But you left several sentenses incomplete. So, I can not fully understood the concept. For example look at the sentenses under "representation in a fixed basis".

Also the sentense " circular basis is defined so that" then it is incomplete.

In the first paragraphs " defination" many words are missed
for example
here, and are the spherical-----

this sentense does not carry the clear meaning.

Please try to complete the description, so it become fully understandable.