Linear Algebra and Optimization with Applications to Machine Learning: Volume I: Linear Algebra for Computer Vision, Robotics, and Machine Learning

Linear Algebra and Optimization with Applications to Machine Learning

by Jean Gallier, Jocelyn Quaintance

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.

Contents: Introduction Vector Spaces, Bases, Linear Maps Matrices and Linear Maps Haar Bases, Haar Wavelets, Hadamard Matrices Direct Sums, Rank-Nullity Theorem, Affine Maps Determinants Gaussian Elimination, LU-Factorization, Cholesky Factorization, Reduced Row Echelon Form Vector Norms and Matrix Norms Iterative Methods for Solving Linear Systems The Dual Space and Duality Euclidean Spaces QR-Decomposition for Arbitrary Matrices Hermitian Spaces Eigenvectors and Eigenvalues Unit Quaternions and Rotations in SO(3) Spectral Theorems in Euclidean and Hermitian Spaces Computing Eigenvalues and Eigenvectors Graphs and Graph Laplacians; Basic Facts Spectral Graph Drawing Singular Value Decomposition and Polar Form Applications of SVD and Pseudo-Inverses Annihilating Polynomials and the Primary Decomposition Bibliography Index

Readership: Undergraduate and graduate students interested in mathematical fundamentals of linear algebra in computer vision, machine learning, robotics, applied mathematics, and electrical engineering.

Genres: Artificial Intelligence

823 pages, Kindle Edition

Published January 22, 2020