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
Solving Ax = b using the Inverse
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- Introduction to Linear Algebra, Gilbert Strang, 2016 (Wellesley-Cambridge Press) - A standard textbook that explains fundamental concepts of linear equations, matrix inversion, and the theoretical solution $x = A^{-1}b$.
- Numerical Linear Algebra, Lloyd N. Trefethen and David Bau III, 1997 (Society for Industrial and Applied Mathematics (SIAM)) DOI: 10.1137/1.9781611971276 - Provides a rigorous treatment of numerical methods for solving linear systems, discussing the efficiency and stability of approaches like Gaussian elimination compared to explicit matrix inversion.
- Linear Algebra (18.06), Gilbert Strang, 2010 (Massachusetts Institute of Technology (MIT) OpenCourseWare) - Offers video lectures and course materials that complement textbook explanations of systems of equations and matrix inverses, available freely online.
- Introduction to Applied Linear Algebra: Vectors, Matrices, and Least Squares, Stephen Boyd and Lieven Vandenberghe, 2018 - Presents an applied perspective on linear algebra, including methods for solving linear systems that are useful in fields like machine learning.