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 nonnegative 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 
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 
6 
Majorisation and doubly stochastic matrices. Perturbation of eigenvalues of normal matrices. Positive definite matrices. Sylvester's law. 
Dr. Tanvi Jain 
6 
Loewner matrices and their eigenvalues. (some recent reserach work that brings together many matrix analysis concepts.) 
Prof. Ravindra B. Bapat 
6 
Graph associated with a matrix, irreducible matrices, PerronFrobenius theorem, primitive, cyclic and reducible matrices, inequalities for Perron root, Mmatrices, eigenproblem over maxalgebra. 
Dr. Krishnan Sivasubramanian 
6 
The adjacency matrix of a graph, a few classical theorems, biclique 
Dr. Shreemayee Bora 
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 13:
 R Bhatia, Matrix Analysis
 R Bhatia, Positive Definite Matrices
 R A Horn and C R Johnson, Matrix Analysis
References for 4 :
 Bapat, R.B. and Raghavan, T.E.S. (1997). Nonnegative Matrices and Applications, Cambridge University Press.
 Horn, R.A. and Johnson, C.R. (1985). Matrix Analysis, Cambridge University Press.
 Minc, H. (1988). Nonnegative Matrices, Wiley.
References for 5 :
 Bapat, R.B. and Raghavan, T.E.S. (1997). Nonnegative Matrices and Applications, Cambridge University Press.
 Biggs. Algebraic Graph Theory, Cambridge University Press; 2nd edition (1994)
 Topics in Algebraic Graph Theory, Cambridge University Press 2005
References for 6:
 D. S. Watkins, Fundamentals of Matrix Computations, 2nd Edn., Wiley, 2002.
 L. N. Trefethen and David Bau, Numerical Linear Algebra, SIAM, 1997.
 G. H. Golub and C.F.Van Loan, Matrix Computation, 3rd Edn., Hindustan book agency, 2007.
TimeTable (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 (3.304.00) 
Tutorial (4.005.00) 
Snacks 5.005.30 


(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