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Eigenwerte von Rotationsmatrizen by Breitsprecher, Arne

Eigenwerte von Rotationsmatrizen

by Arne Breitsprecher
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Book cover type: Paperback
  • ISBN13: 9783668258174
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Grin Verlag
  • Publisher Imprint: Grin Verlag
  • Publication Date:
  • Pages: 20
  • Original Price: USD 22.5
  • Language: German
  • Edition: N/A
  • Item Weight: 55 grams
  • BISAC Subject(s): Vector Analysis

Studienarbeit aus dem Jahr 2016 im Fachbereich Mathematik - Analysis, Note: 2,3, Universität Bremen (Fachbereich 3), Veranstaltung: Mathematische Grundlagen 2, Sprache: Deutsch, Abstract: Dass Mathematik in ihrer Bedeutung mehr als reine Zahlen ist, erkannte bereits der Philosoph und Mathematiker Galilei. Die technischen Entwicklungen der heutigen Zeit stecken voller naturwissenschaftlicher Entdeckungen, Herausforderungen und Problemen. Eines dieser Probleme ist das Eigenwertproblem. So ist die Google Suche abstrahiert eine periodische gigantische Eigenwertaufgabe (PBMW09). Es wird also eine lineare Abbildung gesucht, die sich bei ihrer Transformation nicht verändert oder auf ein Skalar selbst abgebildet wird. Der Skalar wird dann als Eigenwert, der Vektor x als Eigenvektor der Matrix A bezeichnet. Bei diesen Eigenwerten und Vektoren handelt es sich um reelle Eigenwerte von A bzw. reelle Eigenvektoren, weil wir uns im reellen Zahlenbereich bewegen. Es gilt, dass ein Eigenvektor ungleich dem Nullvektor ist, da ansonsten alle λ ∈ R die Gleichung A0 = λ0 erfüllen und damit alle lineare Abbildungen immer in sich selbst überführt würden. Bei Betrachtung im komplexen Zahlenbereich werden die Eigenwerte/-vektoren als komplexe Eigenwerte/-vektoren bezeichnet. Im Folgenden wollen wir uns aber auf die reellen Eigenvektoren beschränken. Als Schlussfolgerung bedeutet dies, dass es keine re-ellen Eigenwerte gibt, au er α ist ein Vielfaches von φ. In diesem Fall entspricht die Rotation einer halben Drehung oder der Identität (ganze Drehung um 360◦).

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