Linear Algebra Fundamentals for Machine Learning
Chapter 1: Why Linear Algebra Matters in Machine Learning
Representing Data with Vectors and Matrices
Linear Algebra in Machine Learning Algorithms
Core Concepts Overview
Setting Up Your Python Environment
Quiz for Chapter 1
Chapter 2: Getting Started with NumPy for Numerical Computing
Introduction to NumPy Arrays
Creating NumPy Arrays
Array Indexing and Slicing
Basic Array Operations
Array Attributes and Shape Manipulation
Hands-on: NumPy Array Creation and Manipulation
Quiz for Chapter 2
Chapter 3: Working with Vectors
What is a Vector?
Vector Notation
Vectors in Python using NumPy
Vector Addition and Subtraction
Scalar Multiplication
Vector Norms: Measuring Length
The Dot Product
Hands-on: Vector Operations with NumPy
Quiz for Chapter 3
Chapter 4: Working with Matrices
What is a Matrix?
Matrix Notation and Dimensions
Matrices in Python using NumPy
Types of Matrices: Square, Identity, Zero
Diagonal and Triangular Matrices
Hands-on: Matrix Creation with NumPy
Quiz for Chapter 4
Chapter 5: Essential Matrix Operations
Matrix Addition and Subtraction
Scalar Multiplication
Matrix Transpose
Matrix Multiplication: The Dot Product
Properties of Matrix Multiplication
Hands-on: Matrix Operations with NumPy
Quiz for Chapter 5
Chapter 6: Systems of Linear Equations and Matrix Inverses
Representing Linear Equations with Matrices
The Concept of a Solution
The Identity Matrix Revisited
The Matrix Inverse
Conditions for Invertibility
Solving Ax = b using the Inverse
Calculating Inverses with NumPy
Solving Linear Systems with NumPy
Hands-on: Solving Systems with NumPy
Quiz for Chapter 6
Introduction to NumPy Arrays
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- The N-dimensional array (ndarray), NumPy community, 2024 - This official guide provides an overview of the
ndarrayobject, explaining its structure, attributes, and efficiency benefits compared to Python lists. - Hands-On Machine Learning with Scikit-Learn, Keras, and TensorFlow: Concepts, Tools, and Techniques to Build Intelligent Systems, Aurélien Géron, 2022 (O'Reilly Media) - This practical guide includes an introduction to NumPy arrays, demonstrating their fundamental role and efficient use in preparing data and performing computations for machine learning models.
- Array programming with NumPy, Charles R. Harris, K. Jarrod Millman, Stéfan J. van der Walt, Ralf Gommers, Pierre Virtanen, David Cournapeau, Eric Wieser, Julian Taylor, Sebastian Berg, Nathaniel J. Smith, Robert Kern, Matti Picus, Stephan Hoyer, Marten H. van Kerkwijk, Matthew Brett, Andrew Haldane, J. Fulton, H. F. Gérard, Edouard Hoppit, F. Mueller, J. Félix, A. Probst, Alexandra Rogozhnikov, Ivan T. Page, and Pauli Virtanen, 2020 Nature, Vol. 585 DOI: 10.1038/s41586-020-2649-2 - This peer-reviewed article outlines the design principles and impact of NumPy, explaining how its array programming model facilitates high-performance scientific computing.