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dc.contributor.authorHoltz, Olga
dc.contributor.authorMehrmann, Volker
dc.contributor.authorSchneider, Hans
dc.description.abstractWe 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.subject.ddc510 Mathematiken
dc.subject.othermatrix functionen
dc.subject.otherdifferential fieldsen
dc.subject.othermatrices that commute with their derivativeen
dc.titleMatrices that commute with their derivative. Research and historical note.en
dc.typeResearch Paperen
tub.publisher.universityorinstitutionTechnische Universität Berlinen
tub.series.issuenumber2012, 22en
tub.series.namePreprint-Reihe des Instituts für Mathematik, Technische Universität Berlinen
tub.affiliationFak. 2 Mathematik und Naturwissenschaften » Inst. Mathematikde
tub.subject.msc200015A27 Commutativityen
tub.subject.msc200015A54 Matrices over function rings in one or more variablesen
Appears in Collections:Technische Universität Berlin » Publications

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