Linear Algebra Essentials for Machine Learning
Chapter 1: Vectors in Machine Learning
Vectors as Data Representations
Fundamental Vector Operations
Vector Magnitude and Direction
The Dot Product and Projections
Vector Norms: Measuring Length
Calculating Distances Between Vectors
Implementing Vector Operations with NumPy
Hands-on Practical: Feature Vector Manipulation
Chapter 2: Matrices: Data Representation and Transformations
Matrices for Organizing Data
Matrix Multiplication Explained
Matrices as Linear Transformations
Representing Systems of Linear Equations
Implementing Matrix Operations with NumPy
Hands-on Practical: Transforming Data Points
Chapter 3: Solving Linear Systems and Matrix Inverses
Linear Systems in Machine Learning Models
Introduction to Gaussian Elimination
Calculating the Inverse of a Matrix
The Determinant and Invertibility
Solving Ax=b using the Inverse
Numerical Stability and Alternatives
Hands-on Practical: Solving for Model Coefficients
Chapter 4: Vector Spaces, Subspaces, and Linear Independence
Linear Combinations and Span
Linear Independence of Vectors
Column Space and Null Space
Hands-on Practical: Analyzing Feature Vector Sets
Chapter 5: Eigenvalues and Eigenvectors
Definition of Eigenvalues and Eigenvectors
The Characteristic Equation
Eigen-decomposition of a Matrix
Significance in Principal Component Analysis (PCA)
Calculating Eigenvalues/Eigenvectors with NumPy
Hands-on Practical: Eigen-decomposition Calculations
Chapter 6: Matrix Decompositions for Machine Learning
Introduction to Matrix Decompositions
Singular Value Decomposition (SVD)
Geometric Interpretation of SVD
SVD for Dimensionality Reduction
SVD Applications in Data Compression
Relationship between SVD and Eigen-decomposition
Overview of LU Decomposition
Overview of QR Decomposition
Implementing Decompositions with SciPy/NumPy
Hands-on Practical: Applying SVD
