tl;dr - a recommendation for a good book that explains the theory behind the auxiliary polynomial/companion matrix methods to solve linear recurrence relations with constant coefficients?
I've bumped into a linear recursive relation problem and it reminded me the auxiliary polynomial technique from basic combinatorics class.
In retrospective, I understand it has to do with Jordan normal forms and Jordan chains. I also checked Wikipedia and found the linear algebra methods, I can see how they are equivalent and why does it work when all the eigenvalues are distinct (and the companion matrix is diagonalizable. Alternatively, the linear system matrix for any initial values is invertible as a Van der Monde matrix). I'm a bit rusty on Jordan normal forms though, so a little help will be great. I tried a few books, mostly those that are referenced from Wikipedia, but they seem to miss this point.
Any reference suggestion will much be appreciated, thanks.