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Lineare Algebra: Ein Grundkurs Mit Aufgabentrainer by Siegfried Bosch

Lineare Algebra: Ein Grundkurs Mit Aufgabentrainer

by Siegfried Bosch
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Book cover type: Paperback
  • ISBN13: 9783662626153
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Springer Spektrum
  • Publisher Imprint: Springer Spektrum
  • Publication Date:
  • Pages: 503
  • Original Price: EUR 37.37
  • Language: German
  • Edition: 6. Aufl. 2021
  • Item Weight: 812 grams
  • BISAC Subject(s): Algebra / Linear

Techniken der Linearen Algebra spielen heute in nahezu allen Gebieten der aktuellen Mathematik eine wichtige Rolle. Demgemä hat sich die Lineare Algebra zu Recht zu einer der tragenden Säulen mathematischer Studien an Universitäten entwickelt.

Dieses bewährte Lehrbuch, das nun in einer überarbeiteten sechsten Auflage vorliegt, repräsentiert in idealer Weise das Pensum einer zweisemestrigen Anfängervorlesung über Lineare Algebra, in deren Zentrum Vektorräume, lineare Abbildungen und Matrizen stehen. Behandelt werden insbesondere lineare Gleichungssysteme und deren Lösung mittels des Gau schen Eliminationsverfahrens, weiter die Eigen- und Normalformentheorie für lineare Selbstabbildungen von Vektorräumen, sowie Skalarprodukte im Rahmen euklidischer und unitärer Vektorräume, einschlie lich der Hauptachsentransformation und des Sylvesterschen Trägheitssatzes. Als Besonderheit wurde die Elementarteilertheorie mit aufgenommen, welche eine sehr effektive Handhabung und explizite Bestimmung von Normalformen quadratischer Matrizen gestattet.

In seiner textlichen Darstellung verfolgt das Buch mehrere Zielsetzungen zugleich. Zunächst liefert es eine klare, systematische und mathematisch strenge, aber dennoch behutsame Entwicklung der Linearen Algebra und ihrer Resultate, zusammen mit den üblichen theoretischen Begriffsbildungen, die diese Theorie so universell einsatzfähig machen. Sodann findet sich zu Beginn eines jeden Kapitels ein informeller Abschnitt mit dem Titel Überblick und Hintergrund als Motivation, der auch die geometrische Anschauung mit einbezieht, wenn immer dies möglich ist. Wie gewohnt enthält das Buch zu jeder thematischen Einheit eine Auswahl an speziell abgestimmten Übungsaufgaben. Zudem wird im Anhang ein neuartiger Aufgabentrainer vorgestellt, der das Bearbeiten der Aufgaben erleichtert und systematisiert. An einer grö eren Anzahl von Beispielen wird demonstriert, wie man mittels Aufgabentrainer zu optimalen Lösungen gelangt. Damit eignet sich das Werk bestens zur Prüfungsvorbereitung und zum Selbststudium.


Prof. Dr. Siegfried Bosch, Westfälische Wilhelms-Universität Münster, Mathematisches Institut

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