AICTE Quality Improvement Programme for 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 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.
Teachers of AICTE approved degree level colleges, industry participants, Students and researchers.
- 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
Registration Fees (to be paid after being shortlisted):
Nil for AICTE-QIP sponsored participants
For others – Industry – INR 10,000/- (ten thousand) + GST @18% per participant
Student – INR 5000/ (five thousand) + GST @18% per participant
To apply, click here and choose the program from under the ‘AICTE QIP’ tab.
Last date to apply is July 15.