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Preface
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)
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
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
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
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
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6. Matrices, Part 2
7. Matrix Applications
8. Matrix Inverse
9. Orthogonal Matrices and QR Decomposition
10. Row Reduction and LU Decomposition
11. General Linear Models and Least Squares
12. Least Squares Applications
13. Eigendecomposition
14. Singular Value Decomposition
15. Eigendecomposition and SVD Applications
16. Python Tutorial