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
Dimensionality Reduction with PCA
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- Principal Component Analysis, I. T. Jolliffe, 2002 (Springer New York) DOI: 10.1007/b98835 - A definitive and comprehensive book on Principal Component Analysis, covering its theory, methods, and applications in detail.
- Pattern Recognition and Machine Learning, Christopher M. Bishop, 2006 (Springer) DOI: 10.1007/978-0-387-45528-0 - A standard textbook that provides a thorough statistical and probabilistic treatment of PCA within the context of machine learning.
- The Elements of Statistical Learning: Data Mining, Inference, and Prediction, Trevor Hastie, Robert Tibshirani, and Jerome Friedman, 2009 (Springer) - A classic reference in statistical learning, with a dedicated chapter explaining PCA as a dimension reduction technique. 2nd edition, available as free PDF.
- Linear Algebra and Learning from Data, Gilbert Strang, 2019 (Wellesley-Cambridge Press) - This book connects core linear algebra concepts, including eigenvectors and eigenvalues, directly to their applications in machine learning, such as PCA. Author's official page.
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