Burnside's Theorem on matrix algebras


Joel H. Shapiro

 

Lecture Notes, May 2014
 
Abstract: Notes for a lecture I gave at the Portland State University Analysis Seminar during the Spring term 2014. The notes describe the 1905 theorem of William Burnside showing that the only irreducible algebra of n x n matrices is the full algebra of all n x n matrices. Also included is the application of this theorem to triangularization of commutative families of matrices.

Download .pdf file (148 KB)