A simple demonstration of the existence of the jordan canonical form for any square matrix

Abstract

All the demonstrations known to this author of the existence of the Jordan Canonical Form aresomewhat complex - usually invoking the use of new spaces, and what not. These demonstrationsare usually too difficult for an average Mathematics student to understand how he or she can obtainthe Jordan Canonical Form for any square matrix. The method here proposed not only demonstratesthe existence of such forms but, additionally, shows how to find them in a step by step manner. I donot claim that the following demonstration is in any way “elegant” (by the standards of elegance infashion nowadays among mathematicians) but merely simple (undergraduate students taking a fistcourse in Matrix Algebra would understand how it works).