Geometric Methods and Applications

Table of Contents

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   Book Overview
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   Chapter 1 Introduction
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   Chapter 2 Basics of Affine Geometry
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   Chapter 3 Properties of Convex Sets: A Glimpse
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   Chapter 4 Embedding an Affine Space in a Vector Space
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   Chapter 5 Basics of Projective Geometry
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   Chapter 6 Basics of Euclidean Geometry
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   Chapter 7 The Cartan-Dieudonné Theorem
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   Chapter 8 The Quaternions and the Spaces S 3 , SU (2), SO (3), and ℝ P 3
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    Chapter 9 Dirichlet-Voronoi Diagrams and Delaunay Triangulations
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    Chapter 10 Basics of Hermitian Geometry
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    Chapter 11 Spectral Theorems in Euclidean and Hermitian Spaces
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    Chapter 12 Singular Value Decomposition (SVD) and Polar Form
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    Chapter 13 Applications of Euclidean Geometry to Various Optimization Problems
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    Chapter 14 Basics of Classical Lie Groups: The Exponential Map, Lie Groups, and Lie Algebras
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    Chapter 15 Basics of the Differential Geometry of Curves
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    Chapter 16 Basics of the Differential Geometry of Surfaces
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    Chapter 17 Appendix