Includes index.

Cover -- Copyright -- Table of Contents -- Preface -- Conventions Used in This Book -- Using Code Examples -- O'Reilly Online Learning -- How to Contact Us -- Acknowledgments -- Chapter 1. Introduction -- What Is Linear Algebra and Why Learn It? -- About This Book -- Prerequisites -- Math -- Attitude -- Coding -- Mathematical Proofs Versus Intuition from Coding -- Code, Printed in the Book and Downloadable Online -- Code Exercises -- How to Use This Book (for Teachers and Self Learners) -- Chapter 2. Vectors, Part 1 -- Creating and Visualizing Vectors in NumPy -- Geometry of Vectors

Operations on Vectors -- Adding Two Vectors -- Geometry of Vector Addition and Subtraction -- Vector-Scalar Multiplication -- Scalar-Vector Addition -- Transpose -- Vector Broadcasting in Python -- Vector Magnitude and Unit Vectors -- The Vector Dot Product -- The Dot Product Is Distributive -- Geometry of the Dot Product -- Other Vector Multiplications -- Hadamard Multiplication -- Outer Product -- Cross and Triple Products -- Orthogonal Vector Decomposition -- Summary -- Code Exercises -- Chapter 3. Vectors, Part 2 -- Vector Sets -- Linear Weighted Combination -- Linear Independence

The Math of Linear Independence -- Independence and the Zeros Vector -- Subspace and Span -- Basis -- Definition of Basis -- Summary -- Code Exercises -- Chapter 4. Vector Applications -- Correlation and Cosine Similarity -- Time Series Filtering and Feature Detection -- k-Means Clustering -- Code Exercises -- Correlation Exercises -- Filtering and Feature Detection Exercises -- k-Means Exercises -- Chapter 5. Matrices, Part 1 -- Creating and Visualizing Matrices in NumPy -- Visualizing, Indexing, and Slicing Matrices -- Special Matrices

Matrix Math: Addition, Scalar Multiplication, Hadamard Multiplication -- Addition and Subtraction -- "Shifting" a Matrix -- Scalar and Hadamard Multiplications -- Standard Matrix Multiplication -- Rules for Matrix Multiplication Validity -- Matrix Multiplication -- Matrix-Vector Multiplication -- Matrix Operations: Transpose -- Dot and Outer Product Notation -- Matrix Operations: LIVE EVIL (Order of Operations) -- Symmetric Matrices -- Creating Symmetric Matrices from Nonsymmetric Matrices -- Summary -- Code Exercises -- Chapter 6. Matrices, Part 2 -- Matrix Norms

Matrix Trace and Frobenius Norm -- Matrix Spaces (Column, Row, Nulls) -- Column Space -- Row Space -- Null Spaces -- Rank -- Ranks of Special Matrices -- Rank of Added and Multiplied Matrices -- Rank of Shifted Matrices -- Theory and Practice -- Rank Applications -- In the Column Space? -- Linear Independence of a Vector Set -- Determinant -- Computing the Determinant -- Determinant with Linear Dependencies -- The Characteristic Polynomial -- Summary -- Code Exercises -- Chapter 7. Matrix Applications -- Multivariate Data Covariance Matrices

If you want to work in any computational or technical field, you need to understand linear algebra. As the study of matrices and operations acting upon them, linear algebra is the mathematical basis of nearly all algorithms and analyses implemented in computers. But the way it's presented in decades-old textbooks is much different from how professionals use linear algebra today to solve real-world modern applications. This practical guide from Mike X Cohen teaches the core concepts of linear algebra as implemented in Python, including how they're used in data science, machine learning, deep learning, computational simulations, and biomedical data processing applications. Armed with knowledge from this book, you'll be able to understand, implement, and adapt myriad modern analysis methods and algorithms. --