## Abstract

In this paper we consider successive orthogonal projections onto m hyperplanes in ℝ^{n}, where m ≥ 2 and n ≥ 2. A limit cycle is defined to be a sequence of points formed by projecting onto each of the hyperplanes once in a prescribed order, with the last projection giving the starting point. Several examples, including triangles, quadrilaterals, regular polygons, and arbitrary collections of lines in ℝ^{2}, are solved for the limit cycle. Limit cycles are found in various ways, including by a limiting process and by solving an mn × mn linear system of equations. The latter approach will produce all the limit cycles for an arbitrary ordered set of m hyperplanes in ℝ^{n}.

Original language | English |
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Pages (from-to) | 201-228 |

Number of pages | 28 |

Journal | Linear Algebra and Its Applications |

Volume | 285 |

Issue number | 1-3 |

DOIs | |

State | Published - Dec 1 1998 |

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