 # Course on Advanced Matrix Algebra and Applications @ IIT Kharagpur [Sept 17-23]: Register by Aug 31

By: Jasmeet | 17 Aug 2019 12:19 PM

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. This course complements the already existing
standard courses such as Matrix Theory and Linear Algebra which do not explore the computational aspects and
applications in detail.

##### Course Objectives

This course is intended for an 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.

##### Course Content
• 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
##### Course Fee

For others – Industry – INR 10,000/- (ten thousand) + GST @18% per participant
Student – INR 5000/ (five thousand) + GST @18% per participant

##### Registration

The last date to register is August 31, 2019.

##### Contact

Phone Number: +91-3222-282856

Email ID: srkhare@maths.iitkgp.ac.in