# Matrix Computation and its applications

By Prof. Vivek K. Aggarwal   |
Learners enrolled: 723
This course deals with applications of matrices to a wide range of areas of engineering and science. Initial some basics of linear algebra is discussed followed by matrix norms and sensitivity and condition number of the matrices. In this course , we will also discuss psudo-inverse of a matrix of any dimension (m x n) using Moore- Penrose theorem. Singular value decomposition of a general matrix is also discussed along with applications. Householder transformations, QR factorization will also be covered.

INTENDED AUDIENCE :UG/PG
PRE-REQUISITES   : Some knowledge of matrix theory
INDUSTRY SUPPORT : Any software/financial industry will be interested.
Summary
 Course Status : Ongoing Course Type : Core Duration : 12 weeks Start Date : 26 Jul 2021 End Date : 15 Oct 2021 Exam Date : 23 Oct 2021 IST Enrollment Ends : 09 Aug 2021 Category : Mathematics Credit Points : 3 Level : Undergraduate/Postgraduate

### Course layout

Module - 1:Some basics of Linear Algebra :- Vector spaces, Linear transformations, eigen values and eigen vectors.
Module - 2:Matrix norm, Sensitivity analysis and condition numbers, Linear systems, Jacobi, Gauss-Seidel and successive over relaxation methods, LU decompositions, Gaussian elimination with partial pivoting, Banded systems, positive definite systems, Cholesky decomposition – sensitivity analysis, Gram- Schmidt orthonormal process, Householder transformation, QR factorization, stability of QR factorization.
Module - 3:Solution of linear least squares problems, normal equations, singular value decomposition (SVD), Moore-Penrose inverse, Rank deficient least squares problems, Sensitivity analysis of least-squares problems, Sensitivity of eigenvalues and eigenvectors.
Module - 4: Reduction to Hessenberg and tridiagonal forms; Power, inverse power and Rayleigh quotient iterations, Explicit and implicit QR algorithms for symmetric and non-symmetric matrices, Reduction to bi diagonal form, Sensitivity analysis of singular values and singular vectors, conjugate gradient method.

### Books and references

(1)B.N. Datta, Numerical Linear Algebra and applications
(2)G. H. Golub and C. F. Van Loan, Matrix Computations
(3)L. N. Trefethen, Numerical Linear Algebra

### Prof. Vivek K. Aggarwal

Dr. Vivek Kumar Aggarwal is presently working as an Assistant Professor dept. of Applied Mathematics, DTU Delhi. He earned his PhD in Mathematics from IIT Kanpur in 2005.

### 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: 23 October 2021 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 8 assignments out of the total 12 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 Madras .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