Applied Linear Algebra

By Prof. Andrew Thangaraj   |   IIT Madras
Learners enrolled: 1876
Introduce the fundamentals of vector spaces, inner products, linear transformations, and eigenspaces to electrical engineering students.

Senior level Undergraduate and First year Postgraduate/PhD
PREREQUISITES : Basic Calculus, Should have done a basic (or a first) course in Linear Algebra
INDUSTRIES  SUPPORT     : Communications, Artificial Intelligence, Analytics
Course Status : Completed
Course Type : Core
Duration : 12 weeks
Category :
  • Electrical, Electronics and Communications Engineering
  • Communication and Signal Processing
  • Control and Instrumentation
Credit Points : 3
Level : Undergraduate/Postgraduate
Start Date : 24 Jan 2022
End Date : 15 Apr 2022
Enrollment Ends : 07 Feb 2022
Exam Date : 23 Apr 2022 IST

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

Page Visits

Course layout

Week 1: Vectors and vector spaces
Week 2:Linear maps I: Definition, Spaces associated with a map, Matrices
Week 3: Linear maps II: Invertible linear maps, Elementary row/column operations, Solving linear equations, Quotient space
Week 4: Linear maps III: Four fundamental spaces, Rank of a matrix, Determinants, Change of basis
Week 5:Eigenvalues and eigenvectors of linear operators
Week 6: Applications of eigenvalues
Week 7:  Inner product spaces
Week 8:Projection and least squares
Week 9:Adjoint of linear maps and operators
Week 10:Self-adjoint and normal operators
Week 11: Positive operators, isometries
Week 12:Polar and singular value decompositions

Click here to view the detailed syllabus

Books and references

Linear Algebra Done Right - Sheldon Axler
Introduction to Linear Algebra - Gilbert Strang
Linear Algebra and Applications - Gilbert Strang
Linear Algebra - Serge Lang
Linear Algebra, S.H. Friedberg, A.J. Insel, and L.E. Spence

Instructor bio

Prof. Andrew Thangaraj

IIT Madras
Andrew Thangaraj received his B.Tech in Electrical Engineering from the Indian Institute of Technology (IIT), Madras, India in 1998 and a PhD in Electrical Engineering from the Georgia Institute of Technology, Atlanta, USA in 2003. He was a post-doctoral researcher at the GTL-CNRS Telecom lab at Georgia Tech Lorraine, Metz, France from August 2003 to May 2004. From June 2004, he has been with the Department of Electrical Engineering, IIT Madras, where he is currently a professor. Since Jan 2012, he has been serving as Editor for the IEEE Transactions on Communications. Since Oct 2011, he has been serving as NPTEL coordinator at IIT Madras. He has played a key role in initiating and running NPTEL online courses and certification. He is currently a National MOOCs Coordinator for NPTEL in the SWAYAM project of the MHRD.

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 April 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.


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

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