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
Matrix Addition and Subtraction
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- Introduction to Linear Algebra, Gilbert Strang, 2016 (Wellesley-Cambridge Press) - A classic textbook providing a comprehensive foundation in linear algebra, including detailed explanations of matrix operations, properties, and their geometric interpretations.
- Linear Algebra and Its Applications, David C. Lay, Steven R. Lay, and Judi J. McDonald, 2020 (Pearson) - This textbook is widely used for its clear explanations and emphasis on applications, making it suitable for readers interested in machine learning. It covers matrix addition and subtraction thoroughly.
- NumPy User Guide: Array basics - Arithmetic operations, NumPy Developers, 2023 - Official documentation for NumPy, illustrating how matrix addition and subtraction are implemented using
ndarrayobjects and standard arithmetic operators. Essential for practical application. - Linear Algebra (18.06SC), Gilbert Strang, 2011 (MIT OpenCourseWare) - A free, online course from MIT that provides video lectures, notes, and problem sets covering fundamental linear algebra concepts, including matrix addition and subtraction.