Geometric Methods and Applications (Hardcover)

Preface.- Introduction.- Basics of Affine Geometry.- Properties of Convex Sets, A Glimpse.- Embedding an Affine Space in a Vector Space.- Basics of Projective Geometry.- Basics of Euclidean Geometry.- The Cartan-Dieudonne Theorem.- Quaternions and Rotations.- Dirichlet-Voronoi Diagrams.- Basics of Hermitian Geometry.- Spectral Theorems.- Singular Value Decomposition (SVD) and Polar Form.- Applications of Euclidean Geometry.- Basics of Classical Lie Groups.- Basics of the Differential Geometry of Curves.- Basics of the Differential Geometry of Surfaces.- Appendix.- Bibliography.- Index.