دانلود کتاب Geometric Linear Algebra Vol.2

فهرست مطالب :

Preface to Volume 1 Preface to Volume 2 Contents PART II. The Euclidean Structures of R^1, R^2 and R^3 Chapter 4. The Euclidean Plane R^2 4.1 Straight Lines 4.2 Circles 4.3 Geometric Definition of the Real Determinant of Order 2 4.4 Nonnatural Inner Products: Positive-Definite and Orthogonal Matrices 4.5 The Singular Value Decomposition: The Polar Decomposition and the Generalized Inverse of a Matrix 4.6 Linear Functional and (Self-)Adjoint Linear Operator 4.7 Diagonalizability of a Symmetric Matrix of Order 2 4.8 The Euclidean Transformation (or Rigid Motion) 4.9 Euclidean Invariants and Euclidean Geometry 4.10 Quadratic curves Chapter 5. The Euclidean Space R^3 5.1 The Exterior (or Vector) Product 5.2 Lines, Planes, and Spheres 5.3 Geometric Definition of the Real Determinant of Order Three 5.4 Nonnatural Inner Products: Positive-Definite and Orthogonal Matrices 5.5 The Singular Value Decomposition: The Polar Decomposition and the Generalized Inverse of a Matrix 5.6 Linear Functional and (Self-) Adjoint Linear Operator 5.7 Diagonalizability of a Symmetric Matrix of Order 3 5.8 The Euclidean Transformation (or Rigid Motion) 5.9 Euclidean Invariants and Euclidean Geometry 5.9.1 Distances from a point to a plane and between planes 5.9.2 Angles between planes 5.9.3 k-parallelogfram: k-vector 5.9.4 The geometry and trigonometry of k-simplex: (tetrahedron) 5.9.5 Barycentric coordinates 5.10 Quadrics 5.11 Elliptic (or Spherical) Geometry 5.12 Hyperbolic Geometry Contents of Volume One Errata to Volume One References 1-19 20-30 31-41 Index of Notations Index