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Eigenvalues

  • Thomas Banchoff
  • John Wermer
Chapter
Part of the Undergraduate Texts in Mathematics book series (UTM)

Abstract

Example 1. Let π be a plane through the origin and let S be the transformation which reflects each vector through π. If Y is a vector on π, then S(Y) = Y, and if U is a vector perpendicular to π, then S(U) = −U. Thus for t = 1 and t = −1, there exist nonzero vectors X satisfying S(X) = tX. If X is any vector which is neither on π nor perpendicular to π, then S(X) is not a multiple of X.

Keywords

Characteristic Equation Linear Transformation Linear Algebra Real Root Orthogonal Matrix 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag New York, Inc. 1992

Authors and Affiliations

  • Thomas Banchoff
    • 1
  • John Wermer
    • 1
  1. 1.Department of MathematicsBrown UniversityProvidenceUSA

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