Matrices that commute with their derivative. Research and historical note.
| dc.contributor.author | Holtz, Olga | |
| dc.contributor.author | Mehrmann, Volker | |
| dc.contributor.author | Schneider, Hans | |
| dc.date.accessioned | 2021-12-17T10:10:18Z | |
| dc.date.available | 2021-12-17T10:10:18Z | |
| dc.date.issued | 2012-07-04 | |
| dc.description.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. | en |
| dc.identifier.issn | 2197-8085 | |
| dc.identifier.uri | https://depositonce.tu-berlin.de/handle/11303/15742 | |
| dc.identifier.uri | http://dx.doi.org/10.14279/depositonce-14515 | |
| dc.language.iso | en | en |
| dc.rights.uri | http://rightsstatements.org/vocab/InC/1.0/ | en |
| dc.subject.ddc | 510 Mathematik | en |
| dc.subject.other | matrix function | en |
| dc.subject.other | differential fields | en |
| dc.subject.other | matrices that commute with their derivative | en |
| dc.title | Matrices that commute with their derivative. Research and historical note. | en |
| dc.type | Research Paper | en |
| dc.type.version | submittedVersion | en |
| tub.accessrights.dnb | free | en |
| tub.affiliation | Fak. 2 Mathematik und Naturwissenschaften::Inst. Mathematik | de |
| tub.affiliation.faculty | Fak. 2 Mathematik und Naturwissenschaften | de |
| tub.affiliation.institute | Inst. Mathematik | de |
| tub.publisher.universityorinstitution | Technische Universität Berlin | en |
| tub.series.issuenumber | 2012, 22 | en |
| tub.series.name | Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin | en |
| tub.subject.msc2000 | 15A27 Commutativity | en |
| tub.subject.msc2000 | 15A54 Matrices over function rings in one or more variables | en |
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