AIS Matrix Analysis (2016) - Speakers and Syllabus

The course will consist of two streams. In one of them, there will be lectures on analysis of matrices, in particular on matrix decompositions, eigenvalues, perturbations and inequalities. In the  other stream, there will be lectures on applications of matrix analysis. In the first two weeks, lectures will be based on non-negative matrices and graph theory. In the third week, there will be lectures on matrix computations.

Syllabus:  Each speaker is required to deliver minimum 6 lectures each of 1 hour duration or 4 lectures each of 1 ½ hour.

Name of the Speaker with affiliation

No. of Lectures

(each of 1 ½ hrs)

Detailed Syllabus

Prof. Rajendra Bhatia
ISI Delhi

6

Bases and orthonormal bases, similarity and unitary similarity, spectral theorem. Singular values, polar decomposition. Norms and approximations. QR Decomposition. Extremal principles for eigenvalues. Perturbation of eigenvalues of Hermitian matrices.

Dr. Priyanka Grover
Shiv Nadar University

6

Majorisation and doubly stochastic matrices. Perturbation of eigenvalues of normal matrices. Positive definite matrices.  Sylvester's law.

Dr. Tanvi Jain
ISI Delhi

6

Loewner matrices and their eigenvalues. (some recent reserach work that brings together many matrix analysis concepts.)

Prof. Ravindra B. Bapat
ISI Delhi

6

Graph associated with a matrix, irreducible matrices, Perron-Frobenius theorem, primitive, cyclic and reducible matrices, inequalities for Perron root, M-matrices, eigenproblem over max-algebra.

Dr. Krishnan Sivasubramanian
IIT Bombay

6

The adjacency matrix of a graph, a few classical theorems, biclique
partitions of a graph, permanents, converting permanent to a determinant
ranking players in a tournament.

Dr. Shreemayee Bora
IIT Guwahati

6

Rotators and Reflectors, QR decomposition by rotators and reflectors, Unitary similarity transformation to upper Hessenberg and tridiagonal forms, Power method and its variations for eigenvalue problems, QR algorithm for eigenvalue problems and its implementation.

 References for 1-3:

  1. R Bhatia, Matrix Analysis
  2. R Bhatia, Positive Definite Matrices
  3. R A Horn and C R Johnson, Matrix Analysis

References for 4 :

  1. Bapat, R.B. and Raghavan, T.E.S. (1997).  Nonnegative Matrices and Applications, Cambridge University Press.
  2. Horn, R.A. and Johnson, C.R. (1985).  Matrix Analysis, Cambridge University Press.
  3. Minc, H. (1988). Nonnegative Matrices, Wiley.

References for 5 :

  1. Bapat, R.B. and Raghavan, T.E.S. (1997).  Nonnegative Matrices and Applications, Cambridge University Press.
  2. Biggs. Algebraic Graph Theory, Cambridge University Press; 2nd edition (1994)
  3. Topics in Algebraic Graph Theory, Cambridge University Press 2005

 References for 6:

  1. D. S. Watkins, Fundamentals of Matrix Computations, 2nd Edn., Wiley, 2002.
  2. L. N. Trefethen and David Bau, Numerical Linear Algebra, SIAM, 1997.
  3. G. H. Golub and C.F.Van Loan, Matrix Computation, 3rd Edn., Hindustan book agency, 2007.

 

Time-Table  (with names of speakers and course associates/tutors):

Day

Date

Lecture 1

(9.30–11.00)

Tea

(11.00–11.30)

Lecturer 2

(11.30–1.00)

Lunch

(1.00–2.30)

Tutorial

(2.30–3.30)

Tea

(3.30-4.00)

Tutorial

(4.00-5.00)

Snacks

5.00-5.30

 

 

(name of the speaker)

 

(name of the speaker)

 

(name of the speaker)

 

(name of the speaker)

 

Mon

2/5/2016

R. Bhatia

 

R. B. Bapat

 

R.B.Bapat

 

R. Bhatia

 

Tues

3/5/2016

R. Bhatia

 

R. B. Bapat

 

R.B.Bapat

 

R. Bhatia

 

Wed

4/5/2016

R. Bhatia

 

R. B. Bapat

 

R.B.Bapat

 

R. Bhatia

 

Thu

5/5/2016

R. Bhatia

 

R. B. Bapat

 

R.B.Bapat

 

R. Bhatia

 

Fri

6/5/2016

R. Bhatia

 

R. B. Bapat

 

R.B.Bapat

 

R. Bhatia

 

Sat

7/5/2016

R. Bhatia

 

R. B. Bapat

 

R.B.Bapat

 

R. Bhatia

 

 SUNDAY

Mon

9/5/2016

P. Grover

 

K. Sivasubramanian

 

P. Grover

 

K. Sivasubramanian

 

Tues

10/5/2016

P. Grover

 

K. Sivasubramanian

 

P. Grover

 

K. Sivasubramanian

 

Wed

11/5/2016

P. Grover

 

K. Sivasubramanian

 

P. Grover

 

K. Sivasubramanian

 

Thu

12/5/2016

P. Grover

 

K. Sivasubramanian

 

P. Grover

 

K. Sivasubramanian

 

Fri

13/5/2016

P. Grover

 

K. Sivasubramanian

 

P. Grover

 

K. Sivasubramanian

 

Sat

14/5/2016

P. Grover

 

K. Sivasubramanian

 

P. Grover

 

K. Sivasubramanian

 

SUNDAY

Mon

16/5/2016

S. Bora

 

T. Jain

 

T. Jain

 

S. Bora

 

Tues

17/5/2016

S. Bora

 

T. Jain

 

T. Jain

 

S. Bora

 

Wed

18/5/2016

S. Bora

 

T. Jain

 

T. Jain

 

S. Bora

 

Thu

19/5/2016

S. Bora

 

T. Jain

 

T. Jain

 

S. Bora

 

Fri

20/5/2016

S. Bora

 

T. Jain

 

T. Jain

 

S. Bora

 

Sat

21/5/2016

S. Bora

 

T. Jain

 

T. Jain

 

S. Bora

 

 

Tutors:

S. No.

Name

Affiliation

1

Dr A. Satyanarayana Reddy

Shiv Nadar University

2

Dr Mushtaq A. Bhat

IIT Bombay

3

Mr Mukesh Kumar Nagar

IIT Bombay

4

Dr Jagjit Singh Matharu

University Institute of Engineering and Technology, Panjab University

5

Dr. Swarup Kumar Panda

ISI Delhi

6

Ms. Nandita Roy

IIT Guwahati

Note: To take full advantage of the Course it is recommended that participants come prepared after reading some basic linear algebra and matrix analysis. The basic text Linear Algebra by K. Hofffman and R Kunze will provide good preparation.(This book is available at very low price in India.) It is especially recommended that you do as many exercises as you can from Chapters 6, 8 and 9 of this book. In addition you could look at the book Linear Algebra Done Right by Sheldon Axler. (This is available free on the Internet)

Click here to download Exercises

You could read Chapter 8 of the book Matrix Analysis by Horn and Johnson, and do exercises from there to be prepared for the lectures by Professors Bapat and Krishnan