Linear Transformations and the Geometry of the Plane

  • Alan Jeffrey


This chapter provides an introduction to the concept of a linear transformation, with initial motivation in this section provided by considering the rotation of orthogonal coordinate systems in two and three space dimensions. A more systematic study of linear transformations will be given in Section 8.3 though there, for simplicity, the discussion will be confined to linear transformations that are of importance when studying the geometry of the Euclidean plane. Even the simple transformations considered in this Chapter are useful, because their geometrical interpretations find applications in topics as diverse as elasticity, crystallography and computer graphics.


Linear Transformation Rotation Matrix Geometrical Effect Counterclockwise Rotation Rigid Body Rotation 
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Copyright information

© Springer Netherlands 2010

Authors and Affiliations

  • Alan Jeffrey
    • 1
  1. 1.University of NewcastleNewcastle upon TyneUnited Kingdom

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