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Ähnliche Matrizen, Eigenwerte, Eigenvektoren by Wolf, Andreas

Ähnliche Matrizen, Eigenwerte, Eigenvektoren

by Andreas Wolf
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Book cover type: Paperback
  • ISBN13: 9783640203130
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Grin Verlag
  • Publisher Imprint: Grin Verlag
  • Publication Date:
  • Pages: 80
  • Original Price: USD 25.5
  • Language: German
  • Edition: N/A
  • Item Weight: 114 grams
  • BISAC Subject(s): Vector Analysis

Studienarbeit aus dem Jahr 2002 im Fachbereich Mathematik - Analysis, Note: 2,0, Johann Wolfgang Goethe-Universität Frankfurt am Main (Professur für Wirtschaftsmathematik - Fachbereich Wirtschaftswissenschaften), Veranstaltung: Seminar "Ausgewählte Gebiete der Analysis und der Linearen Algebra", Sprache: Deutsch, Abstract: (...) Ebenso wie in der vorherigen Arbeit wird auch in unserer Arbeit auf Themen der Linearen Algebra eingegangen, die heute in der Wirtschaftspraxis so häufig wie kein anderes Gebiet der Mathematik angewandt wird. Vor allem die Matrizenrechnung kann auf vielfältige Weise im Rechnungswesen eingesetzt werden, so z. B. in der Kostenrechnung oder im Controlling. Mit Hilfe von linearen Gleichungssystemen werden ökonomische Beziehungen beschrieben und erst durch den Einsatz der linearen Planungsrechnung können ökonomische Entscheidungsprobleme gelöst werden. Unsere Arbeit wird speziell vier Teilgebiete oder Teilaspekte der Linearen Algebra behandeln, die in einem engen Zusammenhang stehen. Als Grundlage für die späteren Ausführungen muss zunächst der Begriff der Determinante erläutert werden. Daran anschlie end wird auf Ähnliche Matrizen eingegangen, die letztlich erst zum Eigenwert und zum Eigenvektor führen. Nach der theoretischen Einführung wird noch einmal ausführlicher auf den Anwendungsbezug oder die praktische Relevanz eingegangen. Denn gerade der Begriff Eigenwert kann in dreierlei Hinsicht angewandt werden. Zunächst spielt der Eigenwert quadratischer, symmetrischer Matrizen eine Rolle im Zusammenhang mit Maximierungs- und Minimierungsaufgaben bei Funktionen mit mehren Variablen. Dann benötigt man für die Behandlung und Lösung von linearen Differenzen- und Differentialgleichungen erster Ordnung grundlegende Kenntnisse über Eigenwerte quadratischer Matrizen und deren Eigenschaften. Und schlie lich kann die Eigenwerttheorie von quadratischen Matrizen dazu genutzt werden, lineare Wachstums- bzw. Ausbreitungsprozesse in der Ökonomie zu beschreiben.

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