Linear Geometry in Euclidean 4-space |
Contents
2Planes in | 1 |
R4 13 Angles between two 2planes in R | 12 |
viii | 29 |
Copyright | |
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Common terms and phrases
algebra angle angle-vector bijection Cartan's theorem Clifford parallel lines Clifford translation complex numbers consequently cross-ratio defined denote e₁ e₂ equivalent Euclidean exists following theorem geometry gonal h₂ Hence homogeneous coordinates identity transformation inner product intersects invariant 2-planes isometry L₂ left Clifford parallel left translation Lemma linear transformation linearly independent linearly independent vectors maximal set mutually isoclinic 2-planes n-space non-singular nonzero vector orientation associated orientation-preserving ortho orthonormal basis pair of 2-planes plane positive definite Proof Proposition prove THEOREM quadric real numbers rectangular coordinate system reflection relative position right translation right-isoclinic satisfies the condition scalar semi-orthogonal sends set of 2-planes set of mutually set of points Suppose u₁ u₂ unique 2-plane containing unit pure quaternions unit vector V₁ V₂ vector space vn+l zero Λ Λ λι