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
Scalar Multiplication
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- Introduction to Linear Algebra, Gilbert Strang, 2016 (Wellesley-Cambridge Press) - This foundational textbook provides thorough coverage of vector spaces and operations, including scalar multiplication, offering rigorous mathematical definitions and geometric intuition.
- Introduction to Applied Linear Algebra: Vectors, Matrices, and Least Squares, Stephen Boyd and Lieven Vandenberghe, 2018 - An excellent resource that presents linear algebra with a strong emphasis on applications, directly relevant to the computational and analytical needs of machine learning practitioners. Covers vector operations from an applied viewpoint.
- NumPy Reference, NumPy Developers, 2025 - The official documentation for NumPy details the array object and its operations, including how scalar multiplication is efficiently implemented in Python for numerical computing.
- Deep Learning, Ian Goodfellow, Yoshua Bengio, and Aaron Courville, 2016 (MIT Press) - This widely recognized textbook includes a dedicated chapter on linear algebra, explaining fundamental vector operations and their direct relevance to algorithms such as gradient descent, where scalar multiplication controls the learning rate.
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