Linear Algebra for Data Science

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This book serves as an introduction to linear algebra for undergraduate students in data science, statistics, computer science, economics, and engineering. The book presents all the essentials in rigorous (proof-based) manner, describes the intuition behind the results, while discussing some applications to data science along the way. The book comes with two parts, one on vectors, the other on matrices. The former consists of four chapters: vector algebra, linear independence and linear subspaces, orthonormal bases and the Gram–Schmidt process, linear functions. The latter comes with eight chapters: matrices and matrix operations, invertible matrices and matrix inversion, projections and regression, determinants, eigensystems and diagonalizability, symmetric matrices, singular value decomposition, and stochastic matrices. The book ends with the solution of exercises which appear throughout its twelve chapters. Request Inspection Copy Sample Chapter(s) Preface Chapter 1: Vector Algebra Chapter 2: Linear Independence and Linear Subspaces Contents: Preface Vectors: Vector Algebra Linear Independence and Linear Subspaces Orthonormal Bases and the Gram–Schmidt Process Linear Functions Matrices: Matrices and Matrix Operations Invertible Matrices and the Inverse Matrix The Pseudo-Inverse Matrix, Projections and Regression Determinants Eigensystems and Diagonalizability Symmetric Matrices Singular Value Decomposition Stochastic Matrices Solutions to Exercises Bibliography Index Readership: Undergraduate course in linear algebra as part of a major in data science, statistics, computer science, economics, and engineering.

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

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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. Sample Chapter(s) Preface Chapter 1: Introduction Request Inspection Copy 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.