Geometric Linear Algebra Vol.2

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