## Linear Geometry in Euclidean 4-space |

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18 pages matching **left translation** in this book

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### Contents

1k Angle1ines of a 2plane relative to another | 22 |

Isometries in Rn and | 65 |

21+ A theorem of E Cartan | 85 |

Copyright | |

13 other sections not shown

### Common terms and phrases

2-plane containing 2-planes A(u 9 cos 9 9 sin 9 algebra angle-vector aqq fo aux1 bijection Cartan's theorem Clifford translation complex numbers conjugate consequently cross-ratio defined denote distance function elements elliptic n-space equivalent Euclidean Euclidean n-space exists following theorem geometry gonal homogeneous coordinates identity transformation induced inner product intersects invariant 2-planes isometry left Clifford parallel left resp left translation Lemma linear transformation linearly independent maximal set mutually isoclinic 2-planes nilpotent non-singular nonzero vector orthonormal basis pair of 2-planes plane positive definite Proof Proposition prove the following prove THEOREM q.Bqq quadric real numbers rectangular coordinate system reflection right translation satisfies the condition scalar semi-orthogonal sends set of mutually set of points shiq subspace Suppose symmetric matrix trans unique 2-plane unit pure quaternions unit vector vector space zero