Advanced Linear Algebra Course | IIT Roorkee | Prof. Premananda Bera
Course Details
| Exam Registration | 366 |
|---|---|
| Course Status | Ongoing |
| Course Type | Core |
| Language | English |
| Duration | 12 weeks |
| Categories | Mathematics |
| 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 | 19 Apr 2026 IST |
| NCrF Level | 4.5 — 8.0 |
Master the Mathematical Backbone of Modern Science: Advanced Linear Algebra
Linear algebra forms the foundational language for a vast array of scientific and engineering disciplines, from quantum mechanics and computer graphics to machine learning and data science. For postgraduate students and professionals looking to deepen their mathematical rigor and computational skills, a structured, advanced course is essential. This is where the Advanced Linear Algebra course, offered by the prestigious Indian Institute of Technology Roorkee (IIT Roorkee), comes into play.
Course Overview: A Deep Dive into Theoretical and Computational Frameworks
This meticulously designed 12-week postgraduate course moves beyond introductory concepts to explore the profound structures of linear algebra. Led by an eminent academic, the course balances theoretical depth with practical computational perspectives, ensuring students gain both intuitive understanding and applicable skills.
Duration: 12 Weeks
Level: Postgraduate
Category: Mathematics
Learn from an Expert: Instructor Profile
The course is taught by Prof. (Dr.) Premananda Bera, a distinguished Professor and the current Head of the Department of Mathematics at IIT Roorkee. With over two decades of teaching experience, Prof. Bera has instructed more than 14 courses in both pure and applied mathematics. His extensive research in computational fluid dynamics and hydrodynamic stability theory, backed by over 35 journal publications, brings a unique applied perspective to theoretical concepts, enriching the learning experience.
Who Should Enroll?
This course is specifically tailored for:
- Master’s students in Mathematics and Physics.
- Third-year B.Tech students in Electrical Engineering and Computer Science.
- Any postgraduate researcher or professional requiring a strong, formal understanding of advanced linear algebraic structures.
Prerequisite: A foundational knowledge of Linear Algebra at the B.Sc. or first/second-year BE level is required.
Detailed Course Curriculum: A 12-Week Journey
The course is systematically laid out to build complexity from fundamental review to advanced topics. Here’s a weekly breakdown of the core modules:
Weeks 1-4: Foundations & Core Structures
- Systems of Linear Equations, Matrix Rank, and Inverses (Review & Advanced Treatment)
- Vector Spaces, Subspaces, Basis, and Dimension: The bedrock of linear algebra.
- Linear Transformations: Existence, representation by matrices, and the Rank-Nullity Theorem.
- Change of Basis and the Algebra of Linear Transformations.
- Dual Spaces, Linear Functionals, and Transpose of a Transformation.
Weeks 5-8: Canonical Forms and Decomposition Theorems
- Characteristic Values, Diagonalization, and Annihilating Polynomials.
- Invariant Subspaces and Triangulation.
- Direct Sum Decompositions and the Primary Decomposition Theorem.
- Jordan Canonical Form and Rational Form: Key to understanding operator structure.
Weeks 9-12: Inner Product Spaces and Advanced Operators
- Inner Product Spaces: Gram-Schmidt Orthogonalization, Orthogonal Complements, Best Approximation.
- Operators on Inner Product Spaces: The Adjoint, Normal, Self-Adjoint, Unitary, and Orthogonal Operators.
- Bilinear and Quadratic Forms.
- The Spectral Theorem and Orthogonal Projections.
- Singular Value Decomposition (SVD) and Generalized Inverses: Cornerstones of modern computational applications.
Essential Reference Textbooks
To support your learning, the course aligns with several authoritative texts:
| Book Title | Author(s) | Publisher |
|---|---|---|
| Linear Algebra (Second Edition) | Kenneth Hoffman, Ray Kunze | Pearson |
| Advanced Linear Algebra (Second Edition) | Steven Roman | Springer |
| Matrix and Linear Algebra | K. B. Datta | Prentice Hall of India |
Why Take This Course?
This course is more than just a syllabus; it's a gateway to advanced research and cutting-edge technology. Understanding Jordan forms is crucial in differential equations and system theory. Mastery of inner product spaces and the Spectral Theorem is indispensable for quantum computing and signal processing. The Singular Value Decomposition (SVD) is a fundamental tool in data science, image compression, and statistical analysis.
Under the guidance of Prof. Premananda Bera, you will not only learn these concepts but also appreciate their interconnectedness and vast applications. This course promises to strengthen your analytical abilities and provide you with the mathematical toolkit needed to tackle complex problems in advanced studies and research.
Enroll today to build an unshakable foundation in the mathematics that powers modern innovation.
Enroll Now →