Geometric Linear Algebra Vol.1

Preface
Contents
PART 1. The Affine and Linear Structures of R^1, R^2 and R^3
Chapter 1.
	1.1 Vectorization of a Straight Line: Affine Structure
		The Vectorization of a straight line
		Linear dependence of line vectors
	1.2 Coordinatization of a Straight Line: R^1 (or R)
		The coordinatization of a straight line
		The real number system R and the standard one-dimensionalvector space R^1
	1.3 Changes of Coordinates: Affine and Linear Transformations (or Mappings)
		Coordinate changes of two vectorized spaces on the same line
	1.4 Affine Invariants
		Affine invariants
Chapter 2. The Two-Dimensional Real Vector Space R^2
	2.1 (Plane) Vector
	2.2 Vectorization of a Plane: Affine Structure
	2.3 Coordinatization of a Plane: R^2
	2.4 Changes of Coordinates: Affine and Linear Transformations (or Mappings)
	2.5 Straight Lines in a Plane
	2.6 Affine and Barycentric Coordinates
	2.7 Linear Transformations (Operators)
	2.8 Affine Transformations
		2.8.1 Matrix representations
		2.8.2 Examples
		2.8.4 Affine geometry
			Menelaus Theorem
			Ceva Theorem
			Desargues Theorem
		2.8.5 Quadratic curves
Chapter 3. The Three-Dimensional Real Vector Space R^3
	3.1 Vectorization of a Space: Affine Structure
	3.2 Coordinatization of a Space: R^3
	3.3 Changes of Coordinates: Affine Transformation (or Mapping)
	3.4 Lines in Space
	3.5 Planes in Space
	3.6 Affine and Barycentric Coordinates
	3.7 Linear Transformations (Operators)
		3.7.1 Linear operators in the Cartesian coordinate system
		3.7.2 Examples
		3.7.3 Matrix representations of a linear operator in various bases
		3.7.4 Linear transformations (operators)
		3.7.5 Elementary matrices and matrix factorizations
		3.7.6 Diagonal canonical form
		3.7.7 Jordan canonical form
		3.7.8 Rational canonical form
	3.8 Affine Transformations
		3.8.1 Matrix representations
		3.8.2 Examples
		3.8.3 Affine invariants
		3.8.4 Affine geometry
Appendix A. Some Prerequisites
	A.1 Sets
	A.2 Functions
	A.3 Fields
	A.4 Groups
	A.5 Polynomials
Appendix B. Fundamentals of Algebraic Linear Algebra
	B.1 Vector (or Linear) Spaces
	B.2 Main Techniques: Linear Combination, Dependence and Independence
	B.3 Basis and Dimension
	B.4 Matrices
	B.5 Elementary Matrix Operations and Row-Reduced Echelon Matrices
	B.6 Determinants
	B.7 Linear Transformations and Their Matrix Representations
	B.8 A Matrix and its Transpose
	B.9 Inner Product Spaces
	B.10 Eigenvalues and Eigenvectors
	B.11 Diagonalizability of a Square Matrix or a Linear Operator
	B.12 Canonical Forms for Matrices: Jordan Form and Rational Form
		B.12.1 Jordan canonical form
		B.12.2 Rational canonical form
References
1-19
20-30
31-41
Index of Notations
Index