TEW  Linear Algebra with applications to data analysis and control (2019)
Speakers and Syllabus
Objectives of the workshop : With exponential growth of computing power and availability of historical data records in digital form is rapidly transforming industrial production systems. As a consequence, applied mathematics and computations have assumed significant importance in design and operation of engineered systems. Linear Algebra and its applications arguably assume a central position in engineering mathematics. While linear algebra related courses are taught in the first year of engineering, students often fail to grasp importance and relevance of this important tool. Thus, it is important to teach linear algebra with “engineering flavour” to students pursuing undergraduate and postgraduate studies engineering. Providing exposure to different engineering applications when various linear algebra tools are taught can help in assimilating ideas better and significantly enhance the learning experience.This course is aimed at teaching various linear algebra techniques with a strong emphasis on engineering applications. The course material will connect important concepts in linear algebra with real world engineering applications, which can be used to motivate UG and PG students.
Syllabus for the lecture series
Name of the speakers with affiliation  Topic  Detailed syllabus 
Harish Pillai EE Department, IIT Bombay 
Solutions of Systems of linear equations 
Linear systems and their solutions  when does a solution exist, how accurate is the solution, how to solve the equations while minimising the error, how to estimate whether the solution obtained is close to the "real" solution. In the process, I would touch on condition number of a matrix, Givens rotations, Householder transforms, LU decomposition. 
Sudhir R. Ghorpade Mathematics Department, IIT Bombay 
Applications of linear algebra to differential equations 
We will begin with a quick review of basics of systems of linear equations and the notions of eigenvalues, eigenvectors and diagonalization of matrices. Then we consider systems of the first order linear differential equations and outline how the methods of linear algebra can be applied to the problem of determining their solutions. We shall also see how this relates to solving homogeneous linear differential equations of nth order. Applications to electrical networks may also be indicated. 
J. K. Verma Mathematics Department, IIT Bombay 
Singular Value decomposition of rectangular matrices 
The singular value decomposition is closely associated with the eigenvalueeigenvector decomposition of symmetric matrices. It applies to any rectangular matrices. It has numerous applications. We shall discuss applications to the least squares problem and polar decomposition of matrices. 
Vikram Gadre Electrical Engineering Department, IIT Bombay 
Transforms in image and signal processing 
Introducing Transforms: Fourier Transform, Wavelet Transform, Radon Transform and generalising to multiple dimensions. Connecting transforms to linear algebra principles and illustration with examples. Mathematical principles of filtering: examples of signal and image filters. 
S. A. Soman Electrical Engineering Department, IIT Bombay 
Least squares approximations and power systems 
Solving Large and Spare Linear Least Squares Problem with Applications to Power System State Estimation. We will explore the following. Overview of Overdetermined Full Rank Linear Least Squares problem. Solving it using normal equations approach and QR decomposition. Sparsity issues and reduction of fill ins during LDU & QR factorisation. Formulation of power system state estimation problem as LSE problem. 
Sachin Patwardhan, Chemical Engineering Department, IIT Bombay 
Applications of singular and eigenvalues 
Module 1 (Applications of Singular Value Decomposition for BigData Analysis) Fault (abnormal behaviour) detection and diagnosis using Principle component analysis (PCA), Fault diagnosis using Fisher Discriminant Analysis, Soft sensor development using Partial Least Squares (PLS), time series modelling using Dynamic PCA. Module 2 (Applications of Eigenvalue based Analysis for Design and Control) Analysis of local stability of engineered systems using local linearisation and eigenvalue based analysis, linear feedback controller synthesis using eigenvalue assignment, convergence of numerical schemes for solving linear algebraic equations using eigenvalue based analysis 
Time Table
Monday 18 Nov 
Tuesday 19 Nov 
Wednesday 20 Nov 
Thursday 21 Nov 
Friday 22 Nov 
Saturday 23 Nov 

9.3011.00  Pillai  Pillai  Verma  Verma  Soman  Soman 
11.0011.15  Tea  
11.1512.45  Ghorpade  Ghorpade  Gadre  Gadre  Patwardhan  Patwardhan 
1.002.30  Lunch  
2.304.30 Lab session 
Pillai Belur Sudarshan Aditya 
Ghorpade Gopi Rekha Ruma 
Verma Belur Sudarshan Aditya 
Gadre Venkitesh Kriti Hiranya 
Patwardhan Venkitesh Kriti Hiranya 
Soman Gopi Rekha Ruma 
4.305.00  Tea  
5.006.00  Bapat*  Belur  Karamchandani  Borkar  Netrapalli  Deshpande 
* To be confirmed 
Lab Instructors
Name  Affiliation  Topics  Dates of the Lab 
Prof. Madhu Belur P. Sudrshan Aditya Nadkarni 
EE Department, IIT Bombay  1. Linear equations 2. Singular Value decomposition 
18 Nov 20 Nov 
Venkitesh Iyer Kriti Goel Hiranya Kishore Dey 
Mathematics Department, IIT Bombay  1. Transforms in image and signal processing 2. Applications of singular and eigenvalues 
21Nov 22Nov 
Gopikrishnan C. R. Rekha Khot Ruma Rani Maity 
Mathematics Department, IIT Bombay  1. ODEs and eigenvalues 2. Least squares approximations 
19Nov 23Nov 
Public Lectures at 5 p.m.
Speaker  Affiliation 
Preneeth Netrapalli  Microsoft Research 
Amit Deshpande  Microsoft Research 
Nikhil Karamchandani  EE, IIT Bombay 
Madhu Belur  EE, IIT Bombay 
Ravindra Bapat  ISI, Delhi 
Vivek Borkar  EE, IIT Bombay 