Linear algebra and optimization with applications to machine learning. Volume 1, Linear algebra for computer vision, robotics, and machine learning [electronic resource] /
Linear algebra for computer vision, robotics, and machine learning
Jean Gallier, Jocelyn Qqaintance.
- Singapore : World Scientific Publishing Co. Pte. Ltd., c2020.
- 1 online resource (824 p.)
Includes bibliographical references and index.
ch. 1. Introduction -- ch. 2. Vector spaces, bases, linear maps -- ch. 3. Matrices and linear maps -- ch. 4. Haar bases, haar wavelets, hadamard matrices -- ch. 5. Direct sums, rank-nullity theorem, affine maps -- ch. 6. Determinants -- ch. 7. Gaussian elimination, LU-factorization, Cholesky factorization, reduced row echelon form -- ch. 8. Vector norms and matrix norms -- ch. 9. Iterative methods for solving linear systems -- ch. 10. The dual space and duality -- ch. 11. Euclidean spaces -- ch. 12. QR-decomposition for arbitrary matrices -- ch. 13. Hermitian spaces -- ch. 14. Eigenvectors and eigenvalues -- ch. 15. Unit quaternions and rotations in SO(3) -- ch. 16. Spectral theorems in euclidean and hermitian spaces -- ch. 17. Computing eigenvalues and eigenvectors -- ch. 18. Graphs and graph laplacians; basic facts -- ch. 19. Spectral graph drawing -- ch. 20. Singular value decomposition and polar form -- ch. 21. Applications of SVD and pseudo-inverses -- ch. 22. Annihilating polynomials and the primary decomposition -- Bibliography -- Index.
"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"--Publisher's website.
System requirements: Adobe Acrobat reader. Mode of access: World Wide Web.