Linear World

Contents
Preface iv
1. Linear Relations 1
1.1. Linear Functions 2
1.2. Linear Equations 7
1.3. Geometric Multiplication 12
2. Linear Geometry 17
2.1. Vector Space 18
2.2. Linear Mappings 27
2.3. Orthogonal Mappings 35
2.4. Biorthogonal Mappings 43
3. Linear Systems 57
3.1. Invertible System 59
3.2. Determined System 63
3.3. Underdetermined System 66
3.4. Overdetermined System 69
4. Quadratic Optimization† 73
4.1. Linear Least Squares 74
4.2. Generalized Inverse 79
4.3. Eigen Value Decomposition 84
5. Linear World 93
6. References 96
A. Linear Axioms 97