Applied Linear Algebra for AI & ML | IIT Kharagpur Course | Prof. Swanand Khare
Course Details
| Exam Registration | 614 |
|---|---|
| Course Status | Ongoing |
| Course Type | Elective |
| Language | English |
| Duration | 12 weeks |
| Categories | Electrical, Electronics and Communications Engineering, Mathematics |
| Credit Points | 3 |
| Level | Undergraduate/Postgraduate |
| Start Date | 19 Jan 2026 |
| End Date | 10 Apr 2026 |
| Enrollment Ends | 02 Feb 2026 |
| Exam Registration Ends | 20 Feb 2026 |
| Exam Date | 25 Apr 2026 IST |
| NCrF Level | 4.5 — 8.0 |
Unlocking AI & ML: The Indispensable Role of Applied Linear Algebra
At the heart of every groundbreaking advancement in Artificial Intelligence (AI) and Machine Learning (ML) lies a robust mathematical foundation. While algorithms and models capture the spotlight, it is the underlying mathematics—particularly Linear Algebra—that provides the essential tools for data representation, model training, and optimization. Recognizing this critical need, the Indian Institute of Technology (IIT) Kharagpur offers a comprehensive 12-week course titled "Applied Linear Algebra in AI and ML," meticulously designed and taught by Prof. Swanand Khare.
Why This Course is Essential for Aspiring AI/ML Practitioners
Linear algebra is far more than just matrix manipulations; it is the language of data. This course bridges the gap between abstract mathematical theory and practical implementation in AI/ML. Unlike traditional linear algebra courses, it is uniquely focused on illustrating how core concepts power real-world applications—from Google's PageRank algorithm to image de-blurring and financial portfolio optimization. For students and professionals in Computer Science, Electrical Engineering, Electronics, Communications, and Mathematics, this course provides the crucial toolkit to understand, develop, and innovate within the AI/ML landscape.
Meet Your Instructor: Prof. Swanand Khare
The course is led by Prof. Swanand Khare, an Associate Professor in the Department of Mathematics and the Centre of Excellence in AI at IIT Kharagpur. With an M.Sc. and Ph.D. from IIT Bombay and post-doctoral research experience at the University of Alberta, Canada, Prof. Khare brings deep expertise in computational linear algebra, inverse eigenvalue problems, and applied statistics. A recipient of the Excellent Young Teacher Award 2018 at IIT Kharagpur, his teaching is informed by active research, ensuring students gain insights into both fundamental principles and cutting-edge applications.
Course Overview & Structure
This undergraduate/postgraduate level course spans 12 weeks, systematically building from foundational concepts to advanced applications. The curriculum is designed to transform theoretical knowledge into practical skill.
Detailed 12-Week Course Layout
| Week | Core Topics Covered |
|---|---|
| Weeks 1-4 | Foundations: Vector spaces, matrices, linear transformations, QR decomposition, and understanding matrix condition numbers for numerical stability. |
| Weeks 5-7 | Least Squares & Estimation: Linear least squares, parameter estimation, classification (applied to datasets like MNIST), multi-objective and constrained least squares with applications in portfolio optimization and image de-blurring. |
| Weeks 8-10 | Eigen-Decompositions & SVD: Spectral theorem, Singular Value Decomposition (SVD), Principal Component Analysis (PCA) for dimensionality reduction, and the Power Method applied to the Google PageRank algorithm. |
| Weeks 11-12 | Advanced Topics & Applications: Sparse solutions, dictionary learning, inverse eigenvalue problems for Markov chains, Low Rank Approximation (LRA), tensor decompositions for deep learning, and matrix completion for collaborative filtering. |
Key Applications You Will Learn
The course's applied focus is its standout feature. Here’s how the math translates to technology:
- Google PageRank: Understand how the Power Method for finding eigenvectors ranks web pages.
- Image De-blurring & Computer Vision: Use regularized least squares and structured low-rank approximations to restore images.
- Principal Component Analysis (PCA): Master SVD to perform dimensionality reduction, crucial for data visualization and noise reduction.
- Financial Modeling: Apply constrained least squares to optimize investment portfolios.
- Recommendation Systems: Learn matrix completion techniques that power platforms like Netflix and Amazon.
- Deep Learning: Explore how tensor decompositions enable efficient sparse learning in neural networks.
Who Should Enroll?
Intended Audience: Senior undergraduate and postgraduate students from Computer Science (CSE), Electrical (EE), Electronics and Communications (ECE), AI, and Mathematics backgrounds.
Prerequisites: A first course in Engineering Mathematics with some prior exposure to basic linear algebra concepts (vectors, matrices). The course is designed to build from these fundamentals.
Recommended Textbooks
- Boyd & Vandenberghe: Introduction to Applied Linear Algebra - Excellent for its focus on vectors, matrices, and least squares.
- Gilbert Strang: Linear Algebra and Learning from Data - Connects linear algebra directly to data science applications.
- David Watkins: Fundamentals of Matrix Computations - A strong resource for computational aspects.
- Golub & Van Loan: Matrix Computations - The classic advanced reference for numerical linear algebra.
Building Your AI/ML Expertise
"Applied Linear Algebra in AI and ML" is more than just a course; it's an investment in your foundational understanding of intelligent systems. In an era driven by data, the ability to manipulate, decompose, and extract meaning from high-dimensional data is paramount. This course, under the guidance of an expert from IIT Kharagpur's prestigious Centre of Excellence in AI, provides the rigorous, application-oriented mathematical training required to excel in research, development, and innovation in the dynamic fields of Artificial Intelligence and Machine Learning.
Enroll Now →