Linear Algebra for Computer Vision & ML by Jean Gallier
Linear Algebra for Computer Vision & ML - Table of Contents
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, Cholesky, Echelon Form
8. Vector Norms and Matrix Norms
9. Iterative 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
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; Primary Decomposition
What You Will Learn in Linear Algebra for Computer Vision & ML
"Linear Algebra for Computer Vision, Robotics, and Machine Learning" by Jean H. Gallier and Jocelyn Quaintance is a mathematically rigorous textbook written for students and researchers working in modern AI-related fields. The book focuses on building a deep theoretical understanding of "linear algebra" concepts that are essential for advanced work in "machine learning", computer vision, and robotics. It is intended for readers who want more than formulas—those who want to understand why the methods work.
The authors carefully develop core topics such as vector spaces, linear maps, inner product spaces, eigenvalues, and the "singular value decomposition (SVD)". Each concept is presented with clear definitions, proofs, and motivation, linking abstract mathematics to real-world applications like dimensionality reduction, coordinate transformations, and data representation. The writing emphasizes precision and clarity, making it suitable for graduate-level study while remaining accessible to motivated readers with a calculus background.
Overall, the book stands out for its theory-first approach and strong connection to practical domains such as "computer vision" and robotics. It is best suited for serious learners, graduate students, and researchers who want a solid mathematical foundation for advanced AI and optimization topics, rather than a quick, application-only guide.
Book Details & Specifications
Title:
Linear Algebra for Computer Vision & ML by Jean Gallier
Publisher:
University of Pennsylvania
Year:
2024
Pages:
787
Type:
PDF
Language:
English
ISBN-10 #:
9811206392
ISBN-13 #:
978-9811206399
License:
External Educational Resource
Amazon:
Amazon
About the Author: Jean Gallier
The author Jean Gallier
is a distinguished mathematician and computer scientist known for his work in "linear algebra", geometry, and theoretical foundations of computing. As a long-time professor at the University of Pennsylvania, he focuses on building strong mathematical frameworks for "machine learning", robotics, and computer vision, emphasizing clarity, rigor, and theory-driven understanding. "Jocelyn Quaintance" is a mathematician and educator recognized for clear mathematical exposition and structured teaching. His collaboration with Gallier blends "academic rigor", "mathematical theory", and practical relevance, producing authoritative resources that support advanced study in "computer vision" and modern AI systems.
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