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Lineare Algebra I by E. Oeljeklaus, R. Remmert

Lineare Algebra I

by E. Oeljeklaus , R. Remmert
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Book cover type: Paperback
  • ISBN13: 9783540067153
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Springer
  • Publisher Imprint: Springer
  • Publication Date:
  • Pages: 282
  • Original Price: GBP 39.99
  • Language: German
  • Edition: N/A
  • Item Weight: 350 grams
  • BISAC Subject(s): Algebra / Linear

3a, mein l}teunb, e5 finb bie stlange U5 ber liingft tJerfc onnen %raum eit; \J1ur bali oft mob erne %riller @aufefn burc ben often @runbton. Sj. Sjeine, tta %roH CstalJut XXVIII) O. Die stiirmische Entwicklung der Mathematik in den letzten Jahrzehnten hat auch vor den Horsalen der Anfangssemester nicht haltgemacht. Galt es in den dreiBiger Jahren noch als revolutionar, Vektorraume in den Grundvorlesungen iiber Analytische Geometrie systematisch zu behandeln, so verstarken sich in jiingster Zeit die Tendenzen, von 'vornherein auch Moduln iiber kommutativen Ringen in die. Begriffsbildungen einzubeziehen, soweit es in Analogie zu Vektorraumen ohne Miihe moglich ist. Fiir diese Entwicklung, an der sich auch das vorliegende Buch orientiert, gibt es eine Reihe inhaltlicher Griinde. So gewinnt man in eleganter und einpragsamer Weise Struktursatze iiber Endomorphismen von Vektorraumen, wenn man den Grundkorper K zum Polynomring K[X] erweitert, den Vektorraum zum K [X]-Modul macht und Satze aus der Modul- theorie (iiber Hauptidealringen) heranzieht. Nicht zuletzt erweist es sich auch in der Determinantentheorie als zweckmaBig, bei der Behandlung des charakteristischen Polynoms den Determinanten- begriffiiber dem Ring K[X] zur Verfugung zu haben. Dieses Taschenbuch ist der erste Teil einer zweibandigen Dar- stellung der Linearen Algebra; es ist aus Vorlesungen entstanden, die der altere Autor vor lahren an den Universitaten Erlangen und Gottingen gehalten hat. 1m vorliegenden Band werden die Grund- lagen der Theorie der Vektorraume und Moduln nebst der zu- gehorigen Abbildungstheorie entwickelt. Die Vektorraumtheorie ist als Spezialfall in der Modultheorie enthalten, sie wird aber nichts- destoweniger auch gesondert und eigenstiindig dargestellt.

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