Applied Linear Algebra Course | IIT Bombay | Prof. Dwaipayan Mukherjee
Course Details
| Exam Registration | 78 |
|---|---|
| Course Status | Ongoing |
| Course Type | Core |
| Language | English |
| Duration | 12 weeks |
| Categories | Electrical, Electronics and Communications Engineering, Communication and Signal Processing, Control and Instrumentation |
| Credit Points | 3 |
| Level | Postgraduate |
| Start Date | 19 Jan 2026 |
| End Date | 10 Apr 2026 |
| Enrollment Ends | 02 Feb 2026 |
| Exam Registration Ends | 20 Feb 2026 |
| Exam Date | 18 Apr 2026 IST |
| NCrF Level | 4.5 — 8.0 |
Unlock the Theoretical Foundations of Modern Engineering with Applied Linear Algebra
Linear algebra is far more than just matrix manipulations; it is the essential language of modern engineering and data science. From the algorithms powering machine learning to the control systems in aerospace engineering, a deep, conceptual understanding of linear algebra is non-negotiable for tackling advanced theoretical problems. This is precisely the gap that the postgraduate course Applied Linear Algebra, offered by the prestigious Indian Institute of Technology Bombay, aims to fill.
Designed and taught by Prof. Dwaipayan Mukherjee, this 12-week intensive program moves beyond numerical computations to train students in the art of mathematical reasoning, proof-writing, and developing critical analytical skills. If you are a graduate student or professional looking to solidify your theoretical foundation for research in cutting-edge fields, this course is your gateway.
Meet Your Instructor: Prof. Dwaipayan Mukherjee
The course is led by an expert with a formidable academic and research background. Prof. Dwaipayan Mukherjee is an Assistant Professor in the Department of Electrical Engineering at IIT Bombay.
- Education: B.E. (Electrical Engineering) from Jadavpur University, M.Tech. (Control Systems) from IIT Kharagpur, and Ph.D. (Aerospace Engineering) from the Indian Institute of Science, Bangalore.
- Research Experience: Postdoctoral work at the Technion - Israel Institute of Technology and research roles at IISc Bangalore.
- Research Interests: Multi-agent systems, cooperative control, and control theory. His expertise ensures the course content is informed by active, frontline research.
Who Should Enroll in This Course?
This course is meticulously designed for a specific audience seeking depth over breadth.
- Primary Audience: Masters and PhD students in Engineering (especially Electrical, Electronics, Communications, Control, and Signal Processing).
- Also Beneficial: Advanced undergraduate students from related disciplines and industry professionals in R&D roles at organizations like ISRO, DRDO, and L&T, which support this course's relevance.
- Ideal For: Those aspiring to solve theoretical problems in control theory, machine intelligence, data science, and signal processing.
Course Philosophy: Theory, Proofs, and Conceptual Clarity
Unlike introductory courses, this program emphasizes:
- The Art of Proof: Developing the ability to prove or disprove mathematical assertions.
- Deep Conceptual Understanding: Moving beyond "how" to compute to "why" the concepts work.
- Abstract Thinking: Leveraging the power of abstraction to gain geometric insights and solve complex problems.
- Critical Thinking: Building a robust mental framework to approach unseen problems in research.
Detailed 12-Week Course Curriculum
The course is structured to build knowledge from fundamental axioms to advanced applications.
| Week | Key Topics Covered |
|---|---|
| Weeks 1-2 | Foundations: Linear Systems, Matrix Forms (RREF), Introduction to Algebraic Structures (Groups, Rings, Fields), Vector Space Definition. |
| Weeks 3-4 | Vector Space Theory: Subspaces, Basis, Dimension, Rank-Nullity Theorem, Coordinates. |
| Weeks 5-6 | Linear Transformations: Properties, Isomorphisms, Dual Spaces, Quotient Spaces, First Isomorphism Theorem. |
| Weeks 7-8 | Inner Product Spaces: Orthogonality, Gram-Schmidt, Projections, Best Approximation (Solving Ax=b), Adjoint Operators. |
| Weeks 9-10 | Eigen-Theory: Eigenvalues/vectors, Diagonalization, Invariant Subspaces, Minimal & Characteristic Polynomials. |
| Weeks 11-12 | Advanced Decompositions & Applications: Jordan Canonical Form, Cayley-Hamilton Theorem, Applications to Graph Theory and Multi-Agent Systems (Consensus, Opinion Dynamics). |
Essential Reference Textbooks
To fully benefit from the course, students are encouraged to refer to two classic texts renowned for their rigorous approach:
- Linear Algebra by Kenneth Hoffman and Ray Kunze
- Linear Algebra Done Right by Sheldon Axler
Why This Course is a Must for Aspiring Researchers
In an era driven by data and complex systems, superficial knowledge of tools is insufficient. This course provides the mathematical maturity required to innovate. Whether you are analyzing stability in control systems, developing a new machine learning algorithm, or modeling network dynamics, the principles taught here—from spectral theory to Jordan decomposition—form the bedrock of advanced engineering research.
By the end of 12 weeks, you will not just know linear algebra; you will be able to think in it. You will be equipped to read advanced research papers, formulate your own theoretical problems, and contribute meaningfully to fields at the intersection of engineering, mathematics, and computer science.
Take the next step in your academic and professional journey. Master the language of modern engineering with Applied Linear Algebra from IIT Bombay.
Enroll Now →