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
Hands-On Practical: Vector Operations in NumPy
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- NumPy User Guide, NumPy Developers, 2024 - This official guide provides detailed information on NumPy arrays, covering creation, basic arithmetic operations (addition, subtraction, scalar multiplication), the dot product (
np.dotand@operator), and linear algebra routines such asnp.linalg.norm. - Introduction to Linear Algebra, Gilbert Strang, 2016 (Wellesley-Cambridge Press) - A widely respected textbook that lays a solid theoretical foundation for vector operations, linear combinations, dot products, and norms, which are fundamental to understanding the mathematics behind the code examples.
- Introduction to Applied Linear Algebra - Vectors, Matrices, and Least Squares, Stephen Boyd and Lieven Vandenberghe, 2018 (Cambridge University Press) - This book presents linear algebra with a focus on applications in engineering and data science, including machine learning. It offers an applied perspective on vector operations, norms, and dot products.
- Python for Data Analysis, Wes McKinney, 2022 (O'Reilly Media) - This authoritative guide for Python data manipulation and analysis offers extensive coverage of NumPy. It provides numerous code examples for array creation and various vector operations, demonstrating how to implement them effectively.
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