Intro; Preface; Acknowledgements; Contents; 1 Low Dimensional Geometric Algebras; 1.1 Linear Algebra Background; Metrics; Euclidean Spaces; Algebras; Exterior Powers and Exterior Algebra; The Projective Space P E; 1.2 GA of the Euclidean Plane, G2; Geometric Algebra; 1.3 GA of the Euclidean Space, G3; Geometric Background; Geometric Algebra; Inner Product and Applications to Vector Algebra; 1.4 GA of the Minkowski Space, G1,3; Clifford Units; Exterior Product and the Canonical Linear Grading of D; The Inner Product; Involutions; Hodge Duality; Relative Space and the Pauli Algebra

1.5 Exercises2 Conformal Geometric Algebra; 2.1 Ground Notions; The Hestenes' Embedding; 2.2 Inner Representations; Spheres; Planes; Circles; Lines; 2.3 Outer Representations; 2.4 Transformations; 2.5 Exercises; 3 Minkowski's Space-Time: Geometry and Physics; 3.1 From Physics to Geometry and Back; Minkowski's View of Special Relativity; Matching Vocabularies: A Mathematical Presentation of Minkowski's Space-Time Geometry; 3.2 A GA View of the Lorentz Group; D-Rotors and Spacetime Isometries; 3.3 A GA View of Electrodynamics; Dirac's Operator; The Lab Picture; Riesz Form of Maxwell's Equations

The Relativistic Lorentz Force LawPotentials; Relative Transformation of the Electromagnetic Field; 3.4 A GA View of Dirac's Equation; 3.5 Exercises; 4 Robot Kinematics; 4.1 Classical Kinematics; 4.2 Forward Kinematics; 4.3 Differential Kinematics; 4.4 Inverse Kinematics; 4.5 Identification of Singularities; 4.6 Exercises; 5 Molecular Geometry; 5.1 Distance Geometry; 5.2 Discretizable Molecular Distance Geometry Problem; 5.3 Cartesian and Internal Coordinates; 5.4 Geometric Algebra Approach; 5.5 Uncertainties from NMR Data; 5.6 Conformal Geometric Algebra Approach

Sphere Intersection with UncertaintiesExample; 5.7 Exercises; References; Index