An Matrix
is a linear transformation (linear Map) Iff, for every pair of
-Vectors and and every Scalar ,

(1) |

(2) |

Consider the 2-D transformation

(3) | |||

(4) |

Rescale by defining and , then the above equations become

(5) |

(6) |

(7) |

variables | type |

Hyperbolic Fixed Point | |

Elliptic Fixed Point | |

Parabolic Fixed Point |

**References**

Woods, F. S. *Higher Geometry: An Introduction to Advanced Methods in Analytic Geometry.* New York: Dover, pp. 13-15, 1961.

© 1996-9

1999-05-25