TEW Linear Algebra and its applications (2020)

Venue:	IIT, Jodhpur, Rajasthan
Date:	19th, Nov 2020 to 13th, Dec 2020

School Convener(s)
Name	Prof. I.K. Rana	Dr. Dilpreet Kaur
Mailing Address	Visiting Faculty Ex Prof. Department of Mathematics, I.I.T. Bombay Visiting Faculty, Center for Basic Sciences Visiting Faculty, NIMS SD School of Sciences	Assistant Professor Indian Institute of Technology Jodhpur NH 65, Surpura Bypass Rd, Karwar, Rajasthan 342037

List of the actual speakers:

S. No.	Name	Position	Affiliation
1.	Prof. I. K. Rana	Ex. Professor	IIT Bombay
2.	Dr. Kiran Hiremath	Associate Professor	IIT Jodhpur
3.	Dr. Sukhendu Ghosh	Assistant Professor	IIT Jodhpur
4.	Dr. Amit Kulshrestha	Associate Professor	IISER Mohali
5.	Dr. Anupam Singh	Associate Professor	IISER Pune
6.	Dr. Gaurav Bhatnagar	Associate Professor	IIT Jodhpur

List of the actual tutors:

S. No.	Name	Position	Affiliation
1.	Dr. Kiran Hiremath	Associate Professor	IIT Jodhpur
2.	Dr. Dilpreet Kaur	Assistant Professor	IIT Jodhpur

List of the Guest Speakers:

S. No.	Name	Position	Affiliation
1.	Dr. Pankaj Yadav	Assistant Professor	IIT Jodhpur
2.	Dr. Chiranjoy Chattopadhyay	Assistant Professor	IIT Jodhpur

Syllabus:

Actual syllabus covered by each speaker:

Name of the Speaker	Time	Detailed Syllabus
Prof. I.K . Rana	All six hours of lectures in Week 1	The following topics were covered with relevant examples. Prof. Rana emphasized on motivation behind all the concepts. Solving system of linear equations, Matrix and Matrix operations. Row Echelon form, Elementary row operations, Inverse of a matrix (Gauss Jordan Method), Rank of a matrix. Vector spaces, Linear span, Linear Independence, Basis and Dimension. Linear Transformations, Matrix representations of linear maps, Rank Nullity Theorem. Inner Product space, orthogonality, Norm, Gram Schmidt Process. Cauchy Schwartz, Triangle inequality, Pythagoras Theorem.
Dr. Kiran Hiremath	First three hours of lectures in Week 2	Linear transformations on a finite-dimensional vector spaces Matrix representation of such linear transformations Properties of such linear transformations and associated spaces like kernel, range, set of linear maps/transformations Rank-Nullity theorem and its proof, its applications Eigenvalues and eigenvectors of the linear transformations, their properties Eigenspace, Caley-Hamilton theorem, minimal polynomial Similarity transformations Diagonalization
Dr. Sukhendu Ghosh	Two hours of lectures in Week 2	Syllabus covered: Differential equations have played an important role in the development of mathematics and physics. A certain set of differential equations is essential to model the applications of real life and technology. Further, one need to know the solution techniques to solve the differential equations for the purpose of mathematical modelling. Knowledge of linear algebra is inevitable for the same. In these lectures, Dr. Bhatnagar have explored the use to linear algebra in differential equations as well as hydrodynamic stability theory. In particular, the following points are discussed: Use of hydrodynamic stability theory in physical and natural applications, Modelling of hydrodynamic problems using differential equations and formulation of eigenvalue problem, Details of the Sturm-Liouville eigenvalue problems, Eigenvalues and eigenfunctions of the boundary value problems (with simple examples of ODE and PDE), Formulation of generalized matrix eigenvalue problem for bounded hydrodynamic flows, Procedure to find out eigenvalues and eigenfunctions of such complex problems and their applications.
Dr. Amit Kulshrestha	One hour lecture in Week 2	Title of Talk: Linear Algebra to Google Google page ranking, linear algebra behind facebook
Dr. Anupam Singh	All six hours of lectures in Week 3	Recall: Linear transformations and their matrix representations. Diagonalizable linear maps, minimal polynomials and characteristic polynomials. Nilpotent and unipotent linear transformations, Jordan decomposition (additive and multiplicative), Jordan canonical form. Primary decomposition theorem, applications of primary decomposition theorem, companion matrices, Rational canonical form. Bilinear forms: Symmetric, skew-symmetric, non-degenerate, congruent matrices, Quadratic forms. Isometries, orthogonal groups, symplectic groups, Hermition forms, Unitary groups. Riesz representation theorem, Normal operators, self-adjoint operators, spectral theorem (for real numbers and complex numbers). Dr. Singh emphasized on motivations behind these topics, he also explained applications of linear algebra in group theory)
Dr. Gaurav Bhatnagar	All six hours of lectures in Week 4	Syllabus covered: While the linear algebra is core to almost all areas of mathematics, it finds many applications in real life as well. One of the advantages of linear algebra over other branches of Mathematics is to introduce the abstract thinking leading towards the interpretations of diverse processes involved in many applications. In these lectures, Dr. Bhatnagar tried to uncover the utility of linear algebra in diverse applications. In particular, the following summarize the lectures delivered by him: The lecture series starts with mentioning the importance of linear algebra in visualizing the fundamental concepts of geometry (such as lines, planes, shapes and rotations) and finance (such as simple and compound interest). Then it talks about its utility in chemical engineering, traffic flow, circuit analysis and cryptography. Also, Graph Theory, a branch of mathematics, may be viewed as basically the application of linear algebra where it enables an efficient way to represent the Graphs. The middle part of the lecture series tries to explore the usage of linear algebra in Image Processing and tries to answer the following: a) Why digital image is represented in form of a matrix? (b) How linear algebra represents the most frequently operations in image processing such as cropping, resizing, rotation and filtering? (c)What is the relationship between colors and linear algebra, ultimately leads to color image processing? he lecture series ends with the introduction of the most versatile factorization technique, Singular Value Decomposition (SVD), and its importance in image demising, image compression and dimensionality-reduction. The widely used technique for dimensionality-reduction, namely, Principle Component Analysis was finally discussed.
Dr. Pankaj Yadav	One hour Guest Lecture in Week 2	Title of Talk: Application of Logistic Regression Models to Investigate Gene-Environment Interaction.
Dr. Chiranjoy Chattopadhyay	One hour Guest Lecture in Week 3	Title of Talk: An introduction to Digital Image Processing through Linear Algebra.

Time Table

Actual time-table that was followed during the programme:

Week-1 of the TEW (November 19-22, 2020)

	(Inauguration and Lecture-I)	(Lecture-II)	(Lecture-III)	(Lecture-IV)	(Lecture-V)	(Tutorial-II)
Date	Thursday Nov. 19, 2020	Friday Nov. 20, 2020	Saturday Nov. 21, 2020	Saturday Nov. 21, 2020	Sunday Nov. 22, 2020	Sunday Nov. 22, 2020
Time	5:00-7:00 pm	5:30-7:00 pm	5:00-6:00 pm	6:15-7:15 pm	4:00-5:00 pm	5:15-7:15 pm
Speaker	IKR	IKR	IKR	IKR	IKR	IKR+DK+KH

Week-2 of the TEW (November 25-29, 2020)

	Guest Lecture	(Inauguration and Lecture-I)	(Lecture-II)	(Lecture-III)	(Lecture-IV)	(Lecture-V)	(Tutorial-II)
Date	Wednesday Nov. 25, 2020	Thursday Nov. 26, 2020	Friday Nov. 27, 2020	Saturday Nov. 28, 2020	Saturday Nov. 28, 2020	Sunday Nov. 29, 2020	Sunday Nov. 29, 2020
Time	5:30-6:30 pm	5:00-7:00 pm	5:30-7:00 pm	5:00-6:00 pm	6:15-7:15 pm	4:00-5:00 pm	5:15-7:15 pm
Speaker	PY	KRH	KRH	SG	SG	AK	SG+DK+KH

Week-3 of the TEW (December 2-6, 2020)

	Guest Lecture	(Inauguration and Lecture-I)	(Lecture-II)	(Lecture-III)	(Lecture-IV)	(Lecture-V)	(Tutorial-II)
Date	Wednesday Dec. 2, 2020	Thursday Dec. 3, 2020	Friday Dec. 4, 2020	Saturday Dec. 5, 2020	Saturday Dec. 5, 2020	Sunday Dec. 6, 2020	Sunday Dec. 6, 2020
Time	5:30-6:30 pm	5:00-7:00 pm	5:30-7:00 pm	5:00-6:00 pm	6:15-7:15 pm	4:00-5:00 pm	5:15-7:15 pm
Speaker	CC	AS	AS	AS	AS	AS	AS+DK+KH

Week-4 of the TEW (December 10-13, 2020)

	(Inauguration and Lecture-I)	(Lecture-II)	(Lecture-III)	(Lecture-IV)	(Lecture-V)	(Tutorial-II) and closing
Date	Thursday Dec. 10, 2020	Friday Dec. 11, 2020	Saturday Dec. 12, 2020	Saturday Dec. 12, 2020	Sunday Dec. 13, 2020	Sunday Dec. 13, 2020
Time	5:00-7:00 pm	5:30-7:00 pm	5:00-6:00 pm	6:15-7:15 pm	4:00-5:00 pm	5:15-7:15 pm
Speaker	GB	GB	GB	GB	GB	GB+DK+KH

Full forms for the abbreviations of speakers and tutors:

IKR : Prof. Inder K. Rana
KH : Dr. Kiran Kumar Hiremath
SG : Dr. Sukhendu Ghosh
AK : Dr. Amit Kulshrestha
GB : Dr. Gaurav Bhatnagar
AS : Dr. Anupam Singh
DK: Dr. Dilpreet Kaur
PY: Dr. Pankaj Yadav
CC: Dr. Chiranjoy Chattopadhayay

List of actual Participants

Serial	SID	Full Name	Gender	Affiliation	Position in College/University	Year of Passing M.Sc./M.A	Ph.D. Degree Date
1	33046	Ms. Tania Sidana	Female	IIIT Delhi	PhD Student	2015
2	33201	Prof Yogesh Sharma	Male	MahilaP.G.College,Jodhpur	Assistant Professor	1998	28/02/2001
3	33266	Mr Prashant Kumar	Male	The LNM Institute of Information Technology	PhD	2015
4	33297	Dr. Meena Kumari Gurjar	Female	Jai Narain Vyas University Jodhpur	Assistant Professor	2008	07/09/2015
5	33485	Ms. Rajni Gupta	Female	St. Stephen's college	Assistant professor	2014
6	33652	Mr Brajamohan Sahoo	Male	Central University of Jharkhand	Msc student	2020
7	33691	Dr. Priyanka Harjule	Female	Indian Institute of Information Technology	Assistant Professor	2012	13/01/2017
8	34149	Dr Ranjit Gangadhar Ghumde	Male	Shri Ramdeobaba college of engineering and management Nagpur	Assistant professor	2006	07/02/2017
9	34153	Mr. Md Hasanuzzaman	Male	Aligarh Muslim University	PhD	2015
10	34159	Dr Yashpreet Kaur	Female	NIT Jalandhar	Asst.Prof.	2013	21/05/2019
11	34199	Ms Shivani Chauhan	Female	Shiv Nadar University	PhD student	2017
12	34217	Ms Khyati Sharma	Female	Shiv Nadar University	PhD	2013
13	34223	Dr Gobinda Chandra Panda	Male	Mahavir institute of engineering and technology, Bhubaneswar	Associate Professor	2005	07/03/2011
14	34228	Mr. Ganesh Jayantrao Dharmadhikari	Male	IISER THIRUVANANTHAPURAM	BS-MS student	2020
15	34237	Ms Raihana Rashid	Female	Central University of Kashmir	Ph. D Scholar	2015
16	34238	Ms Uzma Mubeen	Female	Central University of Kashmir	PhD	2012
17	34241	Mr. Arun Vittal Wandakar	Male	Indian Statistical Institute	B Mat student
18	34248	Mr. Sirish Kumar Dash	Male	Anchalik Mahavidyala Sindhol	Asst. Prof.	2004
19	34257	Mr. Saikat Maity	Male	University of Calcutta	Student
20	34270	Dr. Prasanna Poojary	Male	POORNAPRAJNA COLLEGE UDUPI	PhD	2015	19/03/2020
21	34280	Mr. Debanshu Biswas	Male	Indian Institute of Technology Jodhpur	MSc Student
22	34282	Mr. Aritra Roy	Male	Banaras Hindu University	M.Sc student	2020
23	34299	Mr. Sidhu Jitendra Singh Makkhan	Male	S.G.A.D. College, Khadoor Sahib	Assistant Professor	2010
24	34307	Mr. Dhurai K	Male	Government College of Engineering	Assistant professor	2005
25	34314	Dr. Kulwinder Singh Parmar	Male	I K Gujral Punjab Technical University	Asst Prof	2006	15/10/2014
26	34343	Dr S.Maharasi Maharasi	Female	Sri Parasakthi College for Women, Courtallam	Assistant Professor	2009	07/06/2017
27	34352	Prof. Vijaykumar Jayantibhai Solanki	Male	Government Engineering College Bharuch	Assistant Professor	2009
28	34355	Mr. Akshay Goyal	Male	Department of Mathematics, Aligarh Muslim University	MSc student	2019
29	34374	Prof Sanjeev Kumar	Male	Govt. College Dhaliara (HP)	Asst. Prof.	2015
30	34385	Mr. Jayakumar Koodalingam	Male	DHANALAKSHMI COLLEGE OF ENGINEERING , CHENNAI	ASST. Prof.	2002
31	34387	Mr. Arup Datta	Male	TRIPURA UNIVERSITY (A CENTRAL UNIVERSITY)	MSc Student
32	34455	Mr. Rajkumar D	Male	VELLORE INSTITUTE OF TECHNOLOGY	PhD	2017
33	34462	Mrs S B T Sundari K	Female	Andhra University	Research scholar	2010
34	34514	Mr Vetrivel Veerappan	Male	Mahendra Engineering College (Autonomous)	Assistant Professor	2012
35	34533	Mr. Himanshu Mittal	Male	GD Goenka University, Gurugram	PhD	2016
36		AISHWARAYA		Indian Institute of technology Jodhpur	Ph D student
37		ARNAB KAYAL		Indian Institute of technology Jodhpur	Ph D student
38		SANGHDEEP KISHOR UKEY		Indian Institute of technology Jodhpur	M Sc Student
39		SATPAL		Indian Institute of technology Jodhpur	M Sc Student
40		Sheere Farhat Ansari		Research scholar	Department of Mathematics and Astronomy, University of Lucknow, Lucknow.
41		Shivani		Indian Institute of technology Jodhpur	M Sc Student
42		SUCHAN GHORAI		RAMAKRISHNA MISSION	M Ed Student
43		Tanmay Sahoo		Indian Institute of technology Jodhpur	Ph D student
44		Usha K Sangale		Swami Ramanand Teerth Marathwada University, Nanded (SRTM University)	Assistant Professor

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