Linear Algebra for ML, CV, and Robotics
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References
Preface
Part I — Linear Systems and Subspaces
1
Why Linear Algebra?
2
Systems of Linear Equations
3
Row Reduction and Echelon Forms
4
Vectors in ℝⁿ
Part II — Linear Maps and Coordinate Changes
5
Matrix Equations, Column Space, and Linear Independence
6
Linear Transformations and Their Matrices
7
Affine Transformations and Homogeneous Coordinates
Part III — 3D Geometry for Robotics and Vision
8
3D Rotations and SO(3)
9
Rigid Body Transformations and SE(3)
10
Camera Models and Projection Matrices
11
Projective Geometry and Homography
Part IV — Matrix Factorizations and Eigenstructure
12
LU, Cholesky, Determinants, and Numerical Conditioning
13
Eigenvalues and the Characteristic Equation
14
Diagonalization and the Spectral Theorem
Part V — Orthogonality, Projections, and Least Squares
15
Inner Products and Norms
16
Orthogonal Sets, Gram–Schmidt, and QR
17
Projections, Pseudoinverse, and Least Squares
Part VI — Decompositions and Statistical Geometry
18
Singular Value Decomposition
19
Covariance, Statistical Geometry, and the Matrix Square Root
20
Principal Component Analysis
Part VII — Optimization, Estimation, and Applied 3D Geometry
21
Matrix Calculus
22
Jacobians, Inverse Kinematics, and Nonlinear Optimization
23
State Estimation and Covariance Propagation
24
Lie Groups and Lie Algebras
25
Epipolar Geometry
Appendices
26
Appendix A: Python / NumPy / SciPy / OpenCV Quick Reference
27
Appendix B: Matrix Factorization Summary
28
Appendix C: Rotation Representation Conversions
29
Appendix D: Matrix Calculus Identity Reference
30
Appendix E: Notation Glossary
31
Appendix F: Tensor Notation for Deep Learning
References
References
31
Appendix F: Tensor Notation for Deep Learning