Linear algebra and optimization with applications to machine learning : linear algebra for computer vision, robotics, and machine learning- Vol. 1

1. Introduction 2. Vector Spaces, Bases, Linear Maps 3. Matrices and Linear Maps 4. Haar Bases, Haar Wavelets, Hadamard Matrices 5. Direct Sums, Rank-Nullity Theorem, Affine Maps 6. Determinants 7. Gaussian Elimination, LU-Factorization, Cholesky Factorization, Reduced Row Echelon Form 8. Vector Norms and Matrix Norms 9. Iteractive Methods for Solving Linear Systems 10. The Dual Space and Duality 11. Euclidean Spaces 12. QR-Decomposition for Arbitrary Matrices 13. Hermitian Spaces 14. Eigenvectors and Eigenvalues 15. Unit Quaternions and Rotations in SO(3) 16. Spectral Theorems in Euclidean and Hermitian Spaces 17. Computing Eigenvalues and Eigenvectors 18. Graphs and Graph Laplacians; Basic Facts 19. Spectral Graph Drawing 20. Singular Value Decomposition and Polar Form 21. Applications of SVD and Pseudo-Inverses 22. Annihilating Polynomials and the Primary Decomposition

This book provides the mathematical fundamentals of linear algebra to practicers in computer vision, machine learning, robotics, applied mathematics, and electrical engineering. By only assuming a knowledge of calculus, the authors develop, in a rigorous yet down to earth manner, the mathematical theory behind concepts such as: vectors spaces, bases, linear maps, duality, Hermitian spaces, the spectral theorems, SVD, and the primary decomposition theorem. At all times, pertinent real-world applications are provided. This book includes the mathematical explanations for the tools used which we believe that is adequate for computer scientists, engineers and mathematicians who really want to do serious research and make significant contributions in their respective fields