# Matrix Analysis with Applications

By Prof. S. K. Gupta, Prof. Sanjeev Kumar   |   IIT Roorkee
Learners enrolled: 1668
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.

INTENDED AUDIENCE: UG and PG students of technical universities/colleges
Summary
 Course Status : Completed Course Type : Core Duration : 8 weeks Category : Mathematics Credit Points : 2 Level : Undergraduate/Postgraduate Start Date : 25 Jul 2022 End Date : 16 Sep 2022 Enrollment Ends : 08 Aug 2022 Exam Date : 25 Sep 2022 IST

Note: This exam date is subject to change based on seat availability. You can check final exam date on your hall ticket.

### 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

### Books and references

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

### Prof. S. K. Gupta

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 40 papers in various international journals of repute.

### Prof. Sanjeev Kumar

IIT Roorkee
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 certificate

The course is free to enroll and learn from. But if you want a certificate, you have to register and write the proctored exam conducted by us in person at any of the designated exam centres.
The exam is optional for a fee of Rs 1000/- (Rupees one thousand only).
Date and Time of Exams: 25 September 2022 Morning session 9am to 12 noon; Afternoon Session 2pm to 5pm.
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. If there are any changes, it will be mentioned then.
Please check the form for more details on the cities where the exams will be held, the conditions you agree to when you fill the form etc.

CRITERIA TO GET A CERTIFICATE

Average assignment score = 25% of average of best 6 assignments out of the total 8 assignments given in the course.
Exam score = 75% of the proctored certification exam score out of 100

Final score = Average assignment score + Exam score

YOU WILL BE ELIGIBLE FOR A CERTIFICATE ONLY IF AVERAGE ASSIGNMENT SCORE >=10/25 AND EXAM SCORE >= 30/75. If one of the 2 criteria is not met, you will not get the certificate even if the Final score >= 40/100.

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.

Only the e-certificate will be made available. Hard copies will not be dispatched.

Once again, thanks for your interest in our online courses and certification. Happy learning.

- NPTEL team