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AICTE QIP short term course on
"Advanced Matrix Algebra and Applications"
18 - 22 Sepetember , 2019.
Deparment of Mathematics, IIT Kharagpur.

Time table

Lecture notes

Spectral theorems and applications , Classification of handwritten digits (Dr M Rajesh Kannan)

Linear Algebra (Dr Swanand Khare)

Low rank approximation and applications (Dr Sanand)

Parrallel Computing and Linear systems (Dr Somnath Roy).

Nonnegative matrix factorization and Applications (Mr Jaiprakash)

Lab files can be accessed from here.

AIM: Matrix algebra plays a key role in a lot of application areas such as electrical and electronics engineering, computer science and engineering, industrial engineering to name a few. However, a rigorous course in matrix algebra is usually not taught in many universities and colleges across India. The proposed course complements the already existing standard courses such as Matrix Theory and Linear Algebra which do not explore the computational aspects and applications in details. This course is intended for audience who are mathematicians as well as engineers with a little background in matrix algebra. We provide an introduction to basic concepts in this area and cover important decompositions such as spectral decomposition, LDU, QR and SVD. We illustrate the applications of these decompositions in solving the system of linear equations, least squares problems and eigenvalue problems. Advanced concepts such as the proof of SVD as an application of spectral theorem, condition numbers, sensitivity analysis are also covered which have practical significance. A variety of numerical techniques related to the theory will be discussed. Also, this gives a scope to have some hands on experience on computations using PYTHON.

MAIN TOPICS: Introduction to vectors and matrices, norm, matrix vector multiplication, complexity, Rank, Nullity, Row span, Column span, eigenvalues and eigenvectors of a square matrix, Inner product and orthogonality, Spectral representation of semi-simple matrices, Spectral theorem for symmetric matrices and its applications, Linear equations: Gaussian elimination, LDU decomposition, Cholesky decomposition, Condition number and sensitivity results, QR factorization, Least Squares (LS) problem and solution, Singular Value Decomposition and its applications, Low rank approximations and Sensitivity results for LS problem.

TARGET AUDIENCE: Participants of the program are faculty members, students, working professionals from different institutions, research & development organizations and industries.The course is FREE for faculty members from AICTE institutions, whereas there is a course fee for other participants. However, priority will be given to faculty members of AICTE institutions.

All participants from AICTE Institutions must submit the certificate from the institute authority indicating that the institute is a AICTE institute. All participants (excluding AICTE institutions) will be responsible for all the expenses, including accommodation, travel, and food. However, on the immediate request from the participants, accommodation may be arranged (on self-payment-basis in some hostels/guestrooms) inside the IIT campus. On successful completion of the course, certificate of participation will be issued to all the candidates by the Continuing Education Office, IIT Kharagpur, on the recommendation from the Coordinator. Attendance of each of the candidates will be taken regularly. All the selected participants must bring the original identity card.


ABOUT IIT KHARAGPUR CAMPUS: The Indian Institute of Technology, more commonly known as IITKGP is situated about 120 km west of Kolkata. Kharagpur can be reached in about 2 hours by express trains from Howrah railway station of Kolkata or 3 hours by car from Kolkata Airport. Kharagpur is also connected by direct train services to most major cities of the country. The Institute is about 10 minutes drive (5 km) from the Kharagpur railway station. Private taxi, auto-rickshaw or cycle-rickshaw can be hired to reach the Institute.

Category A. The eligible participants are teachers of AICTE approved degree level Engineering Colleges only.
Category B. Students, Industry/ Institute Sponsored Participants with above mentioned academic background.

Registration: Number of participants for the course will be limited to thirty. The course is free for participants of Category A. The course fee for Sponsored Candidates (Category B) is Rs. 5,000/- for students and Rs. 10,000/- for others. Registration fee includes study materials only.

Accommodation: Category A participants will be provided accommodation in one of the institute Guest Houses free of charge. For others, accommodation may be arranged on payment basis. TA as per rule (Ac-3 tier) will be paid to Category A.

Important Dates:

How to Apply

Procedure for applying in IIT Kharagpur online Course Registration portal Use the link:


Step to be followed:

  1. Sign-Up**
  2. Verify your email-id (link will be send to your e-mail)
  3. Login
  4. Edit Profile (Fill up all the mandatory fields, upload photo and signature)
  5. Click on 'APPLY NOW' button.
  6. Upload your pdf format id-card.
An e-mail will be communicated from the Continuing Education Program, IIT Kharagpur to the shortlisted applicants for completing the registration.
** This is one time sign up process in apply to IIT Kharagpur online Course Registration portal. You can apply to other courses using the same credential.

For any queries please send E-mail to: srkhare@maths.iitkgp.ac.in, rajeshkannan@maths.iitkgp.ac.in