Re: What is the Jordan Separation Theorem and how does it relate to cable companies?

I can only answer the first half of the question (I cannot imagine how the 
theorem is related to cable companies !)

The theorem is the following :

For every square matrix A (NxN), there exists an invertible matrix P (NxN) 
such that, if P' is the inverse matrix of P,

A=PJP'

Where J is a jordan matrix, that is a matrix whose all elements are 0 
except the diagonal ones which are the proper values of A and the super 
diagonal ones which either 0's or 1's. So the Kth row of J is written :

0 0 0 0....m 0 0 0 .... 0 0 0 or 0 0 0 0....m 1 0 0 .... 0 0 0

with m a proper value of A at the Kth position.

For more details and a proof, you may read any good book about matrices 
and/or linear applications (keywords : diagonalisation, jordan form of a 
matrix)