The Z-transform is usually defined and developed in a typical course on Difference Equations. We extend the transform to matrix valued sequences. A couple of key observations leads to a rather novel and simple proof of the Cayley-Hamilton theorem.

Author Bio

Casey Tsai is a first year Master's student at Louisiana State University majoring in Mathematics. She graduates in May 2014. After graduation she plans on pursuing a Ph.D. This project was the continuation of a project she began under Professor Mark Davidson during the SMILE@LSU program in the summer of 2011. She completed the project as a senior.