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Geometric Methods and Applications : For Computer Science and Engineering

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Cover of 'Geometric Methods and Applications : For Computer Science and Engineering'

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 Basic Properties of Convex Sets
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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 Separating and Supporting Hyperplanes
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    Chapter 8 The Cartan–Dieudonné Theorem
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    Chapter 9 The Quaternions and the Spaces S 3 , SU(2), SO(3), and ℝ ℙ 3
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    Chapter 10 Dirichlet–Voronoi Diagrams and Delaunay Triangulations
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    Chapter 11 Basics of Hermitian Geometry
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    Chapter 12 Spectral Theorems in Euclidean and Hermitian Spaces
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    Chapter 13 Singular Value Decomposition (SVD) and Polar Form
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    Chapter 14 Applications of SVD and Pseudo-inverses
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    Chapter 15 Quadratic Optimization Problems
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    Chapter 16 Schur Complements and Applications
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    Chapter 17 Quadratic Optimization and Contour Grouping
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    Chapter 18 Basics of Manifolds and Classical Lie Groups: The Exponential Map, Lie Groups, and Lie Algebras
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    Chapter 19 Basics of the Differential Geometry of Curves
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    Chapter 20 Basics of the Differential Geometry of Surfaces
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    Chapter 21 Appendix
Attention for Chapter 8: The Cartan–Dieudonné Theorem
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