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
Linear Algebra in Machine Learning Algorithms
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- Linear Algebra and Learning from Data, Gilbert Strang, 2019 (Wellesley-Cambridge Press) - A foundational text connecting linear algebra concepts directly to their applications in machine learning and data science, including topics like matrix factorization and PCA.
- Hands-On Machine Learning with Scikit-Learn, Keras, and TensorFlow: Concepts, Tools, and Techniques to Build Intelligent Systems, Aurélien Géron, 2023 (O'Reilly Media) - A practical guide covering various machine learning algorithms, including linear regression and PCA, explaining their underlying mathematical and linear algebra principles. 4th edition.
- NumPy Documentation, NumPy community, 2024 (NumPy) - The official documentation for NumPy, the fundamental Python library for numerical computing that provides efficient array and matrix operations essential for linear algebra in machine learning.
- The Elements of Statistical Learning: Data Mining, Inference, and Prediction, Trevor Hastie, Robert Tibshirani, Jerome Friedman, 2009 (Springer) DOI: 10.1007/978-0-387-84858-7 - A comprehensive textbook offering a statistical and mathematical treatment of machine learning, detailing algorithms like linear regression, PCA, and matrix factorization with their linear algebra foundations. 2nd edition.