Potter, Wielandt, and Drazin on the Matrix Equation AB = ωBA: New Answers to Old Questions
Olga Holtz, Volker Mehrmann, Hans Schneider · American Mathematical Monthly · 2004
1. INTRODUCTION. The aim of this paper is to present a slice of the linear algebra of the 1950s and to give some answers to questions raised by Helmut Wielandt at that time. It was Wielandt’s habit over many years to make notes on papers that interested him in what he called “diaries” (Tageb¨ ucher). These diaries were made available by his family after his death in February 2001 and are currently being transcribed. Many notes therein amount to summaries of papers, but in other cases Wielandt would add questions, ideas, or even further results. In this article we discuss one such entry, which appears on page 35 of Diary VII (1951) and will eventually be accessible in transcribed electronic form [24]. The entry concerns a paper that Wielandt reviewed for the Zentralblatt [23]. We next turn to this paper. In 1950, H. S. A. Potter, a mathematician at Aberdeen University in Scotland, published a note in this MONTHLY [19] on the matrix equation