Linear Algebra Fundamentals for Machine Learning
Chapter 1: Chapter 1: The Building Blocks: Scalars, Vectors, and Matrices
Why Linear Algebra for Machine Learning?
Scalars: The Simplest Objects
Vectors: Points in Space
Matrices: Organizing Data in Grids
Setting Up Your Python Environment
Hands-On Practical: Creating Vectors and Matrices with NumPy
Chapter 2: Chapter 2: Working with Vectors
Vector Addition and Subtraction
Scalar Multiplication
The Dot Product
Vector Norms: Measuring Length
Orthogonal Vectors
Hands-On Practical: Vector Operations in NumPy
Chapter 3: Chapter 3: Working with Matrices
Matrix Addition and Subtraction
Matrix-Scalar Multiplication
Matrix-Vector Multiplication
Matrix-Matrix Multiplication
The Matrix Transpose
Special Types of Matrices
Hands-On Practical: Matrix Operations in NumPy
Chapter 4: Chapter 4: Systems of Linear Equations
Representing Equations in Matrix Form (Ax = b)
The Identity Matrix
The Matrix Inverse
Determinants and Invertibility
Singular vs. Non-Singular Matrices
Hands-On Practical: Solving Systems with NumPy
Chapter 5: Chapter 5: Eigenvalues and Eigenvectors
Matrices as Linear Transformations
Defining Eigenvalues and Eigenvectors
Geometric Interpretation
The Characteristic Equation
Hands-On Practical: Finding Eigenvalues with NumPy
Chapter 6: Chapter 6: Connecting to Machine Learning
Data Representation for Models
Linear Regression as a Matrix Problem
Dimensionality Reduction with PCA
Measuring Similarity with Dot Products
Practice: Data Manipulation with NumPy
Singular vs. Non-Singular Matrices
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- Introduction to Linear Algebra, Gilbert Strang, 2016 (Wellesley-Cambridge Press) - A classic textbook that provides a thorough introduction to linear algebra, defining determinants, matrix invertibility, and their relation to solutions of linear systems.
- Deep Learning (Chapter 2: Linear Algebra), Ian Goodfellow, Yoshua Bengio, Aaron Courville, 2016 (MIT Press) - This chapter details fundamental linear algebra concepts pertinent to machine learning, such as matrix properties, determinants, and their implications for solving linear systems.
- numpy.linalg.det, NumPy Developers, 2023 - Official documentation for NumPy's function that computes the determinant of a matrix, directly supporting the Python code examples provided.
- numpy.isclose, NumPy Developers, 2023 - Official documentation for
numpy.isclose, which explains how to compare floating-point numbers within a tolerance, a method that is essential for numerically stable singularity checks.
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