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
Basic Array Operations
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- The N-dimensional array (ndarray), NumPy Developers, 2023 - Covers fundamental concepts of NumPy arrays, including creation, basic element-wise operations, and an introduction to broadcasting. Essential for beginners.
- Universal functions (ufunc), NumPy Developers, 2023 - Details NumPy's universal functions (ufuncs), explaining how they provide fast, element-wise operations and their underlying mechanics. Provides deeper insight into performance.
- Python for Data Analysis: Data Wrangling with Pandas, NumPy, and IPython, Wes McKinney, 2022 (O'Reilly Media) - A comprehensive guide to data manipulation in Python, dedicating significant sections to NumPy arrays, element-wise operations, broadcasting, and performance considerations. Highly recommended for practical application.