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Classification of Affinities

  • Agustí Reventós Tarrida
Part of the Springer Undergraduate Mathematics Series book series (SUMS)

Abstract

In this and in the following chapter we answer the natural question of how many affine maps there are. To do so we first define an equivalence relation between affine maps and study all the equivalence classes that appear. In low dimensions the problem is not too hard and is solved explicitly in this chapter. The idea is that the classification of affinities is given by the classification of endomorphisms plus a geometrical property: the invariance level.

We shall also give a geometric interpretation of the affinities of the real affine plane

The subsections are
  1. 3.1

    Introduction

     
  2. 3.2

    Similar endomorphisms

     
  3. 3.3

    Similar affinities

     
  4. 3.4

    Computations in coordinates

     
  5. 3.5

    Invariance level

     
  6. 3.6

    Classification of affinities of the line

     
  7. 3.7

    Classification of affinities of the real plane

     
  8. 3.8

    Invariance level in the real plane

     
  9. 3.9

    Geometrical interpretation

     
  10. 3.10

    Decomposition of affinities in the real plane

     
  11. Exercises

     

Keywords

General Homology Characteristic Polynomial Direction Vector Invariance Level Unique Fixed Point 
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.

Bibliography

  1. 8.
    Cedó, F., Reventós, A.: Geometria plana i àlgebra lineal. Collection Manuals of the Autonomous University of Barcelona, vol. 39 (2004) Google Scholar

Copyright information

© Springer-Verlag London Limited 2011

Authors and Affiliations

  1. 1.Department of MathematicsUniversitat Autònoma de BarcelonaBellaterra, BarcelonaSpain

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