Classifying Nilpotent Maps via Partition Diagrams

Summary

This note uses a visual analysis of partition diagrams to give an elementary, pictorial proof of the classification theorem for nilpotent linear maps. We show that any nilpotent map is represented by a matrix with ones in certain positions on the first super-diagonal and zeroes elsewhere.

Additional information

Notes on contributors

Nick Loehr

Nick Loehr ([email protected]) received his Ph.D. in mathematics from the University of California at San Diego. Over the last decade, he has taught mathematics at the College of William and Mary, Virginia Tech, and the United States Naval Academy. His mathematical interests include combinatorics, linear algebra, theoretical computer science, and the interaction between these disciplines. His non-mathematical interests include classical music, classical languages, weightlifting, miniature golf, and molecular biology.