Geometric Methods and Applications - For Computer Science and Engineering

Introduction.- Basics of Affine Geometry.- Basic Properties of Convex Sets.- Embedding an Affine Space in a Vector Space.- Basics of Projective Geometry.- Basics of Euclidean Geometry.- Separating and Supporting Hyperplanes; Polar Duality.- Polytopes and Polyhedra.- The Cartan-Dieudonn´e Theorem.- The Quaternions and the Spaces S3, SU(2), SO(3), and RP3 .- Dirichlet-Voronoi Diagrams.- Basics of Hermitian Geometry.- Spectral Theorems.- Singular Value Decomposition (SVD) and Polar Form.- Applications of SVD and Pseudo-Inverses.- Quadratic Optimization Problems.- Schur Complements and Applications.- Quadratic Optimization and Contour Grouping.- Basics of Manifolds and Classical Lie Groups.- Basics of the Differential Geometry of Curves.- Basics of the Differential Geometry of Surfaces.- Appendix.- References.- Symbol Index.- IndexAppendix.- References.- Symbol Index.- Index