Linear Algebra Fundamentals for Machine Learning
Chapter 1: Chapter 1: The Building Blocks: Scalars, Vectors, and Matrices
Why Linear Algebra for Machine Learning?
Scalars: The Simplest Objects
Vectors: Points in Space
Matrices: Organizing Data in Grids
Setting Up Your Python Environment
Hands-On Practical: Creating Vectors and Matrices with NumPy
Chapter 2: Chapter 2: Working with Vectors
Vector Addition and Subtraction
Scalar Multiplication
The Dot Product
Vector Norms: Measuring Length
Orthogonal Vectors
Hands-On Practical: Vector Operations in NumPy
Chapter 3: Chapter 3: Working with Matrices
Matrix Addition and Subtraction
Matrix-Scalar Multiplication
Matrix-Vector Multiplication
Matrix-Matrix Multiplication
The Matrix Transpose
Special Types of Matrices
Hands-On Practical: Matrix Operations in NumPy
Chapter 4: Chapter 4: Systems of Linear Equations
Representing Equations in Matrix Form (Ax = b)
The Identity Matrix
The Matrix Inverse
Determinants and Invertibility
Singular vs. Non-Singular Matrices
Hands-On Practical: Solving Systems with NumPy
Chapter 5: Chapter 5: Eigenvalues and Eigenvectors
Matrices as Linear Transformations
Defining Eigenvalues and Eigenvectors
Geometric Interpretation
The Characteristic Equation
Hands-On Practical: Finding Eigenvalues with NumPy
Chapter 6: Chapter 6: Connecting to Machine Learning
Data Representation for Models
Linear Regression as a Matrix Problem
Dimensionality Reduction with PCA
Measuring Similarity with Dot Products
Practice: Data Manipulation with NumPy
The Characteristic Equation
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- Introduction to Linear Algebra, Gilbert Strang, 2023 (Wellesley-Cambridge Press) - A widely recognized textbook that thoroughly covers eigenvalues, eigenvectors, and the characteristic equation, with a strong focus on conceptual understanding. (6th Edition)
- 18.06SC Linear Algebra, Gilbert Strang, 2011 (MIT OpenCourseWare) - An open online course offering video lectures and lecture notes by Gilbert Strang, providing a comprehensive and accessible explanation of the characteristic equation and its derivation.
- Mathematics for Machine Learning, Marc Peter Deisenroth, A. Aldo Faisal, Cheng Soon Ong, 2020 (Cambridge University Press) DOI: 10.1017/9781108679901 - This textbook bridges the gap between foundational linear algebra and its specific applications in machine learning, covering eigenvalues and eigenvectors as essential tools. Pages 68-71 specifically cover eigenvalues and eigenvectors.
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