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Courses » Matrix Analysis with Applications

Matrix Analysis with Applications

ABOUT THE COURSE:

This course is offered to UG and PG students of Engineering/Science background. It contains the  concepts related to matrix theory and their applications in various disciplines. It covers a depth  understanding of matrix computations involving rank, eigenvalues, eigenvectors, linear transformation, similarity transformations, (diagonalisation, Jordan canonical form, etc). It also involves various iterative methods, including Krylov subspace methods. Finally, topics like positive matrices, non-negative matrices and polar decomposition are discussed in detail with their applications.

Important For Certification/Credit Transfer:

Weekly Assignments and Discussion Forum can be accessed ONLY by enrolling here

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Note: Content is Free!

All content including discussion forum and assignments, is free


Final Exam (in-person, invigilated, currently conducted in India) is mandatory for Certification and has INR Rs. 1100 as exam fee.


INTENDED AUDIENCE: UG and PG students of technical universities/colleges

CORE/ELECTIVE: Core

UG/PG: UG and PG

PREREQUISITES: NIL

INDUSTRY SUPPORT: NIL

2596 students have enrolled already!!

ABOUT THE INSTRUCTOR:


Dr. S. K. Gupta is an Associate Professor in the Department of Mathematics, IIT Roorkee. His area of expertise includes nonlinear, non-convex and Fuzzy optimization. He has guided three PhD thesis and have published more than 45 papers in various international journals of repute.


Dr. Sanjeev Kumar is working as an associate professor with Department of Mathematics, IIT Roorkee. Earlier, he worked as a postdoctoral fellow with Department of Mathematics and Computer Science, University of Udine, Italy and assistant professor with IIT Roorkee. He is actively involved in teaching and research in the area of computational algorithms, inverse problems and image processing. He has published more than 55 papers in various international journals conferences of repute. He has completed a couple of sponsored research projects and written several chapters in reputed books published with Springer and CRC press.

COURSE LAYOUT:

Week 1  : Echelon form and Rank of a matrix, Solution of system of linear equations.
Week 2  :  Vector spaces and their properties, subspaces, basis and dimension, linear transformations.
Week 3  :  Eigen values and eigen vectors, Calyey Haminton theorem, diagonalization.
Week 4  :  Special matrices, Gerschgorin theorem, inner product spaces, matrix norms and  Gram Schmidt Process
Week 5  :  Normal and Positive Definite matrices, Quadratic forms with applications
Week 6  :  Evaluation of matrix functions, SVD and its applications
Week 7  :  Stationary and non-stationary iterative methods for linear system
Week 8  :  Krylov subspace methods, analysis of positive and non-negative matrices, polar decomposition theorem

SUGGESTED READING MATERIALS:

1. Hoffman, K. and Kunze, R., "Linear Algebra", 2nd edition, Pearson Education (Asia) Pvt. Ltd/ Prentice Hall of India (2004) 
2. Leon, S.J., "Linear Algebra with Applications", 8th Edition, Pearson (2009) 
3. Peter, J. Olever and Shakiban, C., "Applied Linear Algebra", 1st Edition , Prentice Hall (2005) 4. Strang, G., "Linear Algebra and its Applications", 3rd edition, Thomson Learning Asia Pvt Ltd (2003)
4. Strang, G., "Linear Algebra and its Applications", 3rd edition, Thomson Learning Asia Pvt Ltd (2003)
5. Saad, Y., Iterative Methods for Sparse Linear Systems, second edition, SIAM, 2003.
6. Meyer C. D., Matrix Analysis and Applied Linear Algebra, ISBN-10: 0898714540
CERTIFICATION EXAM :
  • The exam is optional for a fee.
  • Date of Exams : October 07 (Sunday)
  • Time of Exams : Morning session 9am to 12 noon; Afternoon session: 2pm to 5pm
  • Exam for this course will be available in both morning & afternoon sessions.
  • Registration url: Announcements will be made when the registration form is open for registrations.
  • The online registration form has to be filled and the certification exam fee needs to be paid. More details will be made available when the exam registration form is published.

CERTIFICATION:

  • Final score will be calculated as : 25% assignment score + 75% final exam score
  • 25% assignment score is calculated as 25% of average of Best 6 out of 8 assignments.
  • E-Certificate will be given to those who register and write the exam and score greater than or equal to 40% final score. Certificate will have your name, photograph and the score in the final exam with the breakup.It will have the logos of NPTEL and IIT Roorkee.It will be e-verifiable at nptel.ac.in/noc.