Geometric Methods and Applications

For Computer Science and Engineering

Authors:

ISBN: 978-1-4419-9960-3 (Print) 978-1-4419-9961-0 (Online)

Table of contents (21 chapters)

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  1. Front Matter

    Pages i-xxvii

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    Book Chapter

    Pages 1-5

    Introduction

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    Book Chapter

    Pages 7-63

    Basics of Affine Geometry

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    Book Chapter

    Pages 65-83

    Basic Properties of Convex Sets

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    Book Chapter

    Pages 85-101

    Embedding an Affine Space in a Vector Space

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    Book Chapter

    Pages 103-175

    Basics of Projective Geometry

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    Book Chapter

    Pages 177-212

    Basics of Euclidean Geometry

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    Book Chapter

    Pages 213-229

    Separating and Supporting Hyperplanes

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    Book Chapter

    Pages 231-280

    The Cartan–Dieudonné Theorem

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    Book Chapter

    Pages 281-300

    The Quaternions and the Spaces S 3, SU(2), SO(3), and ℝ ℙ3

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    Book Chapter

    Pages 301-319

    Dirichlet–Voronoi Diagrams and Delaunay Triangulations

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    Book Chapter

    Pages 321-342

    Basics of Hermitian Geometry

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    Book Chapter

    Pages 343-365

    Spectral Theorems in Euclidean and Hermitian Spaces

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    Book Chapter

    Pages 367-385

    Singular Value Decomposition (SVD) and Polar Form

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    Book Chapter

    Pages 387-410

    Applications of SVD and Pseudo-inverses

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    Book Chapter

    Pages 411-430

    Quadratic Optimization Problems

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    Book Chapter

    Pages 431-437

    Schur Complements and Applications

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    Book Chapter

    Pages 439-457

    Quadratic Optimization and Contour Grouping

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    Book Chapter

    Pages 459-528

    Basics of Manifolds and Classical Lie Groups: The Exponential Map, Lie Groups, and Lie Algebras

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    Book Chapter

    Pages 529-583

    Basics of the Differential Geometry of Curves

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    Book Chapter

    Pages 585-654

    Basics of the Differential Geometry of Surfaces

  22. Back Matter

    Pages 659-680

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