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Main Title: Matrices that commute with their derivative. Research and historical note.
Author(s): Holtz, Olga
Mehrmann, Volker
Schneider, Hans
Type: Research Paper
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.
Subject(s): matrix function
differential fields
matrices that commute with their derivative
Issue Date: 4-Jul-2012
Date Available: 17-Dec-2021
Language Code: en
DDC Class: 510 Mathematik
MSC 2000: 15A27 Commutativity
15A54 Matrices over function rings in one or more variables
Series: Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin
Series Number: 2012, 22
ISSN: 2197-8085
TU Affiliation(s): Fak. 2 Mathematik und Naturwissenschaften » Inst. Mathematik
Appears in Collections:Technische Universität Berlin » Publications

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