Matrix Theory (2023)

Convener(s)

 
Name: Dr. Tanvi Jain Dr. Jagjit Singh
Mailing Address: Associate Professor
Theoretical Statistics and Mathematics Unit, Indian Statistical Institute, New Delhi.		 Assistant Professor
University Institute of Engineering and Technology
Panjab University, Chandigarh
Email: tanvi at isid.ac.in matharuj at pu.ac.in

Matrix theory is a fundamental branch of mathematics having incredibly diverse and far-reaching applications in various fields, including engineering, statistics, computer science, and finance. Its use is critical to many areas of modern science and technology.
The workshop on matrix theory will feature three mini courses from some prominent mathematicians and leading experts in the area. This one-week long event will focus on various aspects of matrix theory, and its connections with Fourier analysis, real and complex analysis and numerical linear algebra to solve problems related to matrices, matrix factorizations and their applications, and the theory of functions that preserve matrix positivity. The programme is aimed at Ph.D. students, post-doctoral fellows and researchers interested in matrix theory and related areas.

Dates: 

Monday, December 18, 2023 - 19:00 to Saturday, December 23, 2023 - 19:00

Venue: 

Venue Address: 

 

 

Panjab University, Sector 25, Chandigarh – 160014

 

 

Venue State: 

Venue City: 

PIN: 

160014

Chrono Order: 

461

Syllabus: 

 Syllabus to be covered in terms of modules of 6 lectures each :

Name of the Speakers with their affiliation.

No. of
Lectures

Detailed Syllabus

Professor Rajendra Bhatia

Department of Mathematics Ashoka University, Haryana

6 hrs

Use of Fourier Analysis to solve some problems of matrix theory: Computation of norms of some infinite matrices like the Hilbert matrix, Cesaro matrix, etc. as well as of the Toeplitz and Hankel matrices. Some generalizations of these that are useful in number theory. Solutions of the Sylvester Equation using Fourier analysis. Positive definite sequences and functions, and their use in deriving matrix inequalities.

Professor Peter Semrl

Institute of Mathematics, Physics and Mechanics, Slovenia,

3 hrs

From Loewner's characterization of operator monotone functions to fundamental theorem of chronogeometry:
 
Local order isomorphisms of matrix and operator domains will be discussed. A connection with Loewner's theorem and the fundamental theorem of chronogeometry will be explained. The first one characterizes operator monotone functions while the second one describes the general form of bijective preservers of light-likeness on the classical Minkowski space. We will present an improvement of the fundamental theorem of chronogeometry.

Professor Shreemayee Bora

Department of Mathematics IIT, Guwahati

9 hrs

LU factorization:
Gaussian Elimination as an LU factorization of a matrix; Existence and uniqueness of LU factorization; computing LU factors; variants of LU factorization; Cholesky factorization of positive definite matrices: Positive definite matrices and their properties; existence and uniqueness of Cholesky factorization of positive definite matrices and its relationship with LU factorization; computing Cholesky factors;

QR factorizations of matrices: Existence and uniqueness of QR factorizations of matrices; computing QR factors; applications of QR factorizations; relationship of QR factorizations with other factorizations;

Polar decompositions of matrices: Existence of polar decompositions; relationship with other decompositions; their applications;

Singularvaluedecompositionsofmatrices:Existenceanduniqueness, properties and applications. Relationship with other decompositions. Decompositions related to the matrix eigenvalue problem:Diagonalizability; Jordan canonical form (in brief);Schur's

Theorem (real and complex versions); spectral theorems; a brief introduction to computing eigenvalues and eigenvectors for dense matrices.

Dr. Apoorva Khare

Associate Professor
Department of Mathematics
IISC, Bangalore

4.5 hrs

Entrywise positivity preservers: Theory of functions preserving matrix
positivity. Positivity and total positivity of matrices, classical results of
Schoenberg and Karlin; inertia of matrices; classical results on
entrywise powers as well as some recent developments on positivity

Dr. Tanvi Jain

Associate Professor
Theoretical Statistics and
Mathematics Unit,
Indian Statistical Institute,
New Delhi.

4.5 hrs

 

References:

  1. Rajendra Bhatia, Positive Definite Matrices, Princeton university press,2007.

  2. Rajendra Bhatia, Fourier Series (Classroom Resource Materials), Cambridge university press,2005.

  3. D. S. Watkins, Fundamentals of Matrix Computation, 2nd Edition, Wiley,2002.

  4. R. A. Horn and C. R. Johnson, Matrix Analysis, CUP,1985.

  5. Apoorva Khare, Matrix Analysis and Entrywise Positivity Preservers, Hindustan book agency, 82,2022.

  6. L. N. Trefethen and David Bau, Numerical Linear Algebra, SIAM,1997.

  7. G. H. Golub and C. F. Van Loan, Matrix Computation, 3rd edition., Hindustan book agency,2007

 

 Names of the tutors with their affiliation:

  1. Dr. Yogesh Kapil, Assistant Professor, SLIET, Longowal, Punjab,INDIA.

  2. Dr. Jagjit Singh, Assistant Professor, UIET, Panjab University, Chandigarh.

 

Time Table: 

Tentative time-table, mentioning names of the speakers and tutors with their affiliation:

Day

Date

Lecture 1

(9.30–11.00)

Tea

(11.05–11.25)

Lecture 2

(11.30–1.00)

Lunch

(1.05–1.55)

Lecture 3

(2.00–3.30)

Tea

(3.35-3.55)

Discussion

(4.00-5.00)

Mon

18/12

SB

 

RB

 

TJ

 

JS/YK

Tues

19/12

SB

 

RB

 

TJ

 

JS/YK

Wed

20/12

SB

 

RB

 

TJ

 

JS/YK

Thu

21/12

SB

 

PS

 

AK

 

JS/YK

Fri

22/12

PS

 

SB

 

AK

 

JS/YK

Sat

23/12

AK

 

SB

 

RB

 

JS/YK


Full forms for the abbreviations of speakers and tutors:
RB: Professor Rajendra Bhatia
PS: Professor Peter Semrl
SB: Professor Shreemayee Bora AK: Dr. Apoorva Khare
TJ: Dr. Tanvi Jain YK: Dr. Yogesh Kapil JS: Dr. Jagjit Singh

 

Selected Applicants: 

 

Sr.n SID Full Name Gender Affiliation Position in College/ University University/ Institute M.Sc./ M.A. Year of Passing M.Sc./ M.A Ph.D. Degree Date
1 51579 Ms Neha Singh Female NA NA National institute of technology calicut 2023  
2 51431 Ms. Mamta Verma Female Dr B R Ambedkar National Institute of Technology Jalandhar PhD Research Scholar Akal University, Talwandi Sabo 2022  
3 51589 Dr. Mushtaq Ahmad Bhat Male NIT Srinagar Assistant Professor University of Kashmir 2011 31 Oct 2015
4 51803 Mr. Anshul Prajapati Male Indian Institute of Technology Delhi Research Scholar Indian Institute of Technology Delhi 2019  
5 51497 Mr. Nepur Ranjan Hazarika Male COTTON UNIVERSITY PhD Student COTTON UNIVERSITY 2022  
6 51815 Mr. Kannan R Male Indian Institute of Technology Guwahati Phd Bharathiar University 2019  
7 51879 Dr. Ravinder Kumar Male Dr B R Ambedkar NIT Jalandhar Asst .Prof. HPU Shimla/HPU Campus/M.Sc. 2009 25 May 2016
8 52051 Mr H Lal Hriatpuia Male Mizoram University PhD M.Sc. 2023  
9 52094 Mr Pranab Modak Male Mizoram university Phd Burdwan university 2020  
10 52095 Ms. Anju Rani Female Sant Longowal Institute of Engineering and Techology research Scholar Sant Longowal Institute of Engineering and Techology 2019  
11 52098 Mr. Mandeep Prajapati Male Sant Longowal Institute of Engineering and Technology Ph.D. Punjabi University Patiala 2017  
12 52289 Mr. Md Sohidul Alam Male IIT Guwahati PhD Calcutta University 2020  
13 52517 Mr. Balasubramannyan S Male Indian Institute of Technology Guwahati PhD Cochin University of Science and Technology 2020  
14 52744 Ms. Mohit Mohit Female University of Delhi PhD student University of Delhi 2019  
15 52915 Ms. Ruchi Garg Female Department of Mathematics , University of Delhi PhD Student Hindu College, University of Delhi 2021  
16 52961 Ms. Manisha Chhillar Female University of Delhi PhD University of Delhi 2021  
17 52966 Mr Rajat Adak Male Indian Institute of Technology Hyderabad MSc Student Indian Institute of Technology Hyderabad Appeared / Awaiting Result  
18 53182 Dr. Tejbir Lohan Male Institute of Mathematical Sciences Chennai Visiting position IIT Kanpur 2018 5 Sep 2023
19 53146 Mr. Bharat Pratap Chauhan Male Shiv Nadar Institution of Eminence, Delhi-NCR, India PhD HANSRAJ COLLEGE, UNIVERSITY OF DELHI, NEW DELHI 2018  
20 53226 Mr. Krishna Kumar Gupta Male Shiv Nadar Institution of Eminence, PhD Indian Institute of Technology, Madras 2019  
21 53374 Mr. Juganta Rajkhowa Male Tezpur University PhD Student Tezpur University 2023  
22 53458 Mr. Susobhan Mazumdar Male St. Joseph's University, Bengaluru Assistant Professor Indian Institute of Technology, Madras/ Indian Institute of Technology/ M.Sc 2010  
23 53478 Mr Mohammed Shameem Male National Institute of Technology (NIT) Calicut PhD IIT Palakkad 2023  
24 53556 Mr. Saikat Patra Male Indian Institute of Science Education and Research, Berhampur PhD Student UNIVERSITY OF CALCUTTA 2018  
25 53527 Mr Saurabh Dwivedi Male Shiv Nadar Institute of eminence PhD university of hyderabad 2023  
26 53589 Mr. Dushyant Kumar Sengar Male SHIV NADAR UNIVERSITY PhD INDIAN INSTITUTE OF TECHNOLOGY KANPUR 2020  
27 53607 Mr. Saptak Bhattacharya Male Indian Statistical Institute, Delhi Centre PhD student Jadavpur University 2021  
28 53642 Ms Bhumika Choudhary Female Sant Longowal Institute of Engineering and Technology Research Scholar SANT LONGOWAL INSTITUE OF ENGINEERING AND TECHNOLOGY 2022  
29 53823 Mr. Sujit Sakharam Damase Male Indian Institute of Science PhD student IIT Madras 2021  
30 53167 Mr. Manish Pal Male Atal Bihari Vajpayee Govt Degree College, Sunni Asst. Professor Himachal Pradesh University, Shimla 2018  
  Local Participants      
1 53573 Mr. Rifat Siddique Male IISER Mohali PhD IISER Mohali 2023  
2 53550 Ms. Sanchita Satpathy Female IISER Mohali Int-phd student IISER Mohali Appeared / Awaiting Result  
3 51617 Ms Kirti Kajla Female PANJAB UNIVERSITY RESEARCH SCHOLAR University of Delhi 2019  
  Waiting list Participants   
1 53845 Dr. Bihalan Bhattacharya Male Indian Institute of Science Education and Research, Berhampur Post Doctoral Fellow Indian School of Mines, Dhanbad 2015 8 Sep 2023
2 52526 Mr Keshav Saini Male Malaviya National Institute of Technology Jaipur PhD Malaviya National Institute of Technology Jaipur 2022  
3 51734 Mr Arindam Sutradhar Male University of Louisiana at Lafayette, Completed Ph.D. in August 2023. PhD IISER Kolkata   4 Aug 2023
4 51350 Mr Mukesh Chandra Karmi Male DA-IICT Gandhinagar, Gujarat PHD SCHOLAR NATIONAL INSTITUTE OF TECHNOLOGY ROURKELA 2020 23 Jul 2023

 

 

 

 

 

How to Reach: 

TBA

School Short Name: 

mt

Last Date Application: 

Saturday, November 18, 2023

School Type: 

NCMW

Separate faculty form: 

0