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
Representing Linear Equations with Matrices
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- Introduction to Linear Algebra, Gilbert Strang, 2016 (Wellesley-Cambridge Press) - This classic textbook is widely used for introductory linear algebra courses. It comprehensively covers the representation of linear systems in matrix form (Ax=b) as a fundamental concept.
- Introduction to Applied Linear Algebra - Vectors, Matrices, and Least Squares, Stephen Boyd, Lieven Vandenberghe, 2018 (Cambridge University Press) DOI: 10.1017/9781108583664 - This textbook offers a practical, applied approach to linear algebra with a strong focus on computation and applications, aligning well with the machine learning context. It thoroughly covers systems of linear equations and their matrix representation.
- 18.06SC Linear Algebra (Fall 2011), Gilbert Strang, 2011 - This widely recognized online course provides comprehensive video lectures and lecture notes covering the fundamental concepts of linear algebra, including the representation of systems of linear equations in matrix form (Ax=b).