Linear Algebra for Machine Learning and Data Science Course Syllabus

Overview: This course provides a practical introduction to linear algebra with a focus on applications in machine learning and data science. Designed for beginners, it spans approximately 34 hours over four weeks, requiring 8–10 hours per week. Through hands-on exercises and real-world examples, learners will build a solid foundation in vectors, matrices, linear transformations, and eigenvalues, culminating in a portfolio-ready project. The course emphasizes both theoretical understanding and practical implementation using industry-relevant tools.

Module 1: Systems of Linear Equations

Estimated time: 8 hours

• How matrices arise from systems of equations
• Operations on systems of equations
• Singularity and its implications
• Linear dependence and independence
• Determinants and their properties

Module 2: Vector and Matrix Operations

Estimated time: 8 hours

• Vector representation and arithmetic (sum, difference, scalar multiplication)
• Dot product and its geometric interpretation
• Matrix types and operations
• Matrix inverse and its applications
• Practical use of determinants

Module 3: Linear Transformations

Estimated time: 9 hours

• Concept and definition of linear transformations
• Representing transformations using matrices
• Geometric interpretations of matrix transformations
• Applying transformations in machine learning contexts

Module 4: Eigenvalues and Eigenvectors

Estimated time: 9 hours

• Definition and computation of eigenvalues and eigenvectors
• Significance in data analysis
• Application to Principal Component Analysis (PCA)
• Using eigenvectors for dimensionality reduction

Module 5: Final Project

Estimated time: 10 hours

• Implement a PCA-based data compression model
• Analyze real-world dataset using linear algebra techniques
• Submit a report demonstrating conceptual understanding and code implementation

Prerequisites

• Basic high school algebra
• Familiarity with Python programming (helpful but not required)
• Basic understanding of functions and graphs

What You'll Be Able to Do After

• Represent data as vectors and matrices effectively
• Apply matrix operations like inverse, determinant, and dot product in ML contexts
• Interpret matrix properties such as rank and linear independence
• Use eigenvalues and eigenvectors to solve machine learning problems
• Implement linear algebra techniques in practical data science projects