Numerical Linear Algebra Course | NPTEL IIT Roorkee | Prof. P.N. Agrawal & Prof. D.N. Pandey
Course Details
| Exam Registration | 70 |
|---|---|
| Course Status | Ongoing |
| Course Type | Elective |
| Language | English |
| Duration | 12 weeks |
| Categories | 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 | 19 Apr 2026 IST |
| NCrF Level | 4.5 — 8.0 |
Unlock the Power of Matrices: A Deep Dive into Numerical Linear Algebra
In the digital age, where data drives innovation, a strong foundation in Numerical Linear Algebra is no longer a luxury—it's a necessity. From the algorithms that power search engines and image recognition to the simulations that design aircraft and forecast weather, matrices are the silent workhorses of modern science and engineering. Recognizing this critical need, the prestigious National Programme on Technology Enhanced Learning (NPTEL) offers a comprehensive course, Numerical Linear Algebra, delivered by distinguished faculty from IIT Roorkee.
This meticulously structured 12-week program is designed to transform your understanding of matrix computations, moving from theoretical concepts to practical, stable numerical algorithms used in real-world applications.
Meet Your Expert Instructors from IIT Roorkee
The course is led by two accomplished academicians with a wealth of teaching and research experience, ensuring you learn from the best.
Prof. P. N. Agrawal is a Professor in the Department of Mathematics at IIT Roorkee. With research expertise in Approximation Theory and Complex Analysis, he is a seasoned educator. Prof. Agrawal has previously delivered 13 video lectures on Engineering Mathematics for NPTEL and has supervised nine Ph.D. theses. With over 187 research publications, he brings deep scholarly insight to the course.
Prof. D. N. Pandey, an Associate Professor in the same department, complements the instruction with his specialization in semigroup theory and functional differential equations. An experienced educator having worked at BITS-Pilani and LNMIIT, Prof. Pandey has authored a book and published more than 60 research papers. He has also created e-content for UGC's e-Pathshala, highlighting his commitment to quality digital pedagogy.
Who Should Enroll in This Course?
This course is specifically intended for:
- Undergraduate (UG) and Postgraduate (PG) students of Engineering (all branches).
- UG and PG students of Science (Mathematics, Physics, Computer Science, Data Science).
- Researchers and professionals looking to solidify their fundamentals in numerical matrix computations.
- Anyone preparing for competitive exams or seeking a career in data science, machine learning, computational physics, or control systems.
Course Overview: What Will You Learn?
Spanning 12 intensive weeks, the course curriculum is designed to build your knowledge from the ground up, covering both the "what" and the "how" of numerical linear algebra.
Detailed 12-Week Course Layout
| Week | Core Topics Covered |
|---|---|
| Week 1-3 | Foundations: Matrix operations, vector spaces, linear transformations, eigenvalues, eigenvectors, and diagonalization. |
| Week 4 | Computational Basics: Orthogonalization (Gram-Schmidt), introduction to MATLAB, and computer representation of numbers (crucial for understanding numerical error). |
| Week 5-7 | Error & Stability: Floating-point arithmetic, round-off errors, conditioning, condition numbers, vector/matrix norms, and stability analysis of algorithms. |
| Week 8-10 | Matrix Decompositions & Applications: Deep dive into Singular Value Decomposition (SVD), its algebraic/geometric properties, least squares solutions, and perturbation theory. |
| Week 11-12 | Advanced Algorithms: Householder transformations, QR factorization method, Power method for eigenvalues, and the Jacobi method. |
Why is This Knowledge So Valuable?
The concepts taught in this course are not abstract mathematics; they are the building blocks for countless technologies:
- Control Theory & Dynamical Systems: Analyzing system stability and designing controllers.
- Image & Signal Processing: Compression (using SVD) and filtering techniques.
- Data Science & Machine Learning: Principal Component Analysis (PCA) is fundamentally SVD. Recommender systems and many ML algorithms rely heavily on matrix computations.
- Numerical Analysis & Scientific Computing: Solving large systems of equations efficiently and accurately.
Recommended Textbooks for Further Study
To supplement the video lectures, the instructors recommend the following authoritative texts:
- V. Sundarapandian, Numerical Linear Algebra, PHI, 2008.
- Biswa Nath Dutta, Numerical Linear Algebra and Applications, SIAM, 2010.
- Roger A. Horn and Charles R. Johnson, Matrix Analysis, Cambridge University Press, 1994.
- William Ford, Numerical Linear Algebra with Applications, Academic Press, 2014.
Enroll Today and Build a Critical Skill Set
The Numerical Linear Algebra course by IIT Roorkee on the NPTEL platform represents a unique opportunity to learn a foundational subject from top-tier instructors at no cost. Whether you aim to excel in academics, boost your research capabilities, or enhance your professional profile for the data-driven industry, this course provides the rigorous training you need. Master the mathematics behind the machines and unlock new possibilities in your academic and professional journey.
Enroll Now →