Hindawi Publishing Corporation Advances in Difference Equations Volume 2008, Article ID 867635, 6 pages doi:10.1155/2008/867635 Research Article Reducibility and Stability Results for Linear System of Difference Equations Aydin Tiryaki 1 and Adil Misir 2 1 Department of Mathematics and Computer Sciences, Faculty of Arts and Science, Izmir University, 35340 Izmir, Turkey 2 Department of Mathematics, Faculty of Arts and Science, Gazi University, Teknikokullar, 06500 Ankara, Turkey Correspondence should be addressed to Adil Misir, adilm@gazi.edu.tr Received 8 August 2008; Revised 22 October 2008; Accepted 29 October 2008 Recommended by Martin J. Bohner We first give a theorem on the reducibility of linear system of difference equations of the form xn  1 Anxn. Next, by the means of Floquet theory, we obtain some stability results. Moreover, some examples are given to illustrate the importance of the results. Copyright q 2008 A. Tiryaki and A. Misir. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 1. Introduction Consider the homogeneous linear system of difference equations xn  1 Anxn, n ∈ N  {0, 1, 2,...}, 1.1 where Ana ij n is a k × k nonsingular matrix with real entries and xnx 1 n, x 2 n,...,x k n T ∈ R k . If for some n 0 ≥ 0, xn 0  x 0 1.2 is specified, then 1.1 is called an initial value problem IVP. The solution of this IVP is given by x ( n, n 0 ,x 0 )   n−1  in 0 Ai  x 0 : Φnx 0 , 1.3