direkt zum Inhalt springen

direkt zum Hauptnavigationsmenü

Sie sind hier

TU Berlin

Inhalt des Dokuments

Preprint 22-2012

Matrices that commute with their derivative. Research and historical note.

Source file is available as :   Portable Document Format (PDF)

Author(s) : Olga Holtz , Volker Mehrmann , Hans Schneider

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 22-2012

MSC 2000

15A27 Commutativity
15A54 Matrices over function rings in one or more variables

Abstract :
We examine when a matrix whose elements are differentiable functions in one variable commutes with its derivative. This problem was discussed in a letter from Issai Schur to Helmut Wielandt written in 1934, which we found in Wielandt's Nachlass. We present this letter and its translation into English. The topic was rediscovered later and partial results were proved. However, there are many subtle observations in Schur's letter which were not obtained in later years. Using an algebraic setting, we put these into perspective and extend them in several directions. We present in detail the relationship between several conditions mentioned in Schur's letter and we focus in particular on the characterization of matrices called Type 1 by Schur. We present several examples that demonstrate Schur's observations.

Keywords : matrix function, differential fields, matrices that commute with their derivative

Zusatzinformationen / Extras


Schnellnavigation zur Seite über Nummerneingabe