Module 4 : Solving Linear Algebraic Equations
Section 9 : Appendix A: Behavior of Solutions of Linear Difference Equations
 
Now, consider set of $n$ equations
MATH --------(198)
which can be rearranged as
MATH --------(199)
--------200)
Using above identity, it can be shown that
MATH --------(201)
and the solution of equation (178) reduces to
MATH --------(202)

and MATH as MATH if and only if MATH The largest magnitude eigen value, i.e., $\rho (\QTR{bf}{B})$ will eventually dominate and determine the rate at which MATH The result proved in this section can be summarized as follows: