ISL Linear Algebra (2014)

Venue: CEMS, SSJ Campus, Kumaun University, Almora
Dates: 17th – 29th March, 2014


Convener(s) Speakers, Syllabus and Time table Applicants/Participants


School Convener(s)

Name D. P. Patil H.S.Dhami Sanjay K Pant
Mailing Address Department of Mathematics,
Indian Institute of Science,
Vice-chancellor, Kumaun University,
 Nainital 263001
Deen Dayal Upadhyaya College, University of Delhi, Karampura, New Delhi-110015


Speakers and Syllabus 


Module I (Vector Spaces)
Lecture I-1(Vector Spaces):Vector spaces, Subspaces, Linear System of equations, Gauss Elimination.
Lecture I-2(Bases and Dimension): Generating systems, Bases and Dimensions of vector spaces.
Lecture I-3(Linear Maps): Linear Maps, Space of Linear maps, Linear maps and bases.
Lecture I-4(Affine Spaces): Affine spaces and affine subspaces, Affine maps, reflections,rotations, Affine groups, Description of affine groups in dimension 2 and 3.
Lecture I-5(The rank theorem): The rank theorem, Direct sums and projections.
Lecture I-6(Dual Spaces): Dual spaces, dual bases, dual of a linear map, hyperplanes, Quotient spaces, codimension, isomorphism theorems, Group actions.
Instructor :
Prof. J.K. Verma(JKV), Department of Mathematics, IIT Bombay-400076 (jkv at
Tutor : TBA

Module II (Matrices and Determinants)
Lecture II-1(Matrices): The matrix of a linear map, relation to change of bases, inverties, transpose, Rank of matrices, row rank, column rank.
Lecture II-2(Elementary Matrices): Elementary matrices, Elementary operations.
Lecture II-3(Determinants): Permutations, Canonical decomposition, Signature, Symmetric and Alternative groups, Multi-linear maps, Determinant functions.
Lecture II-4(Computational Rules): Computational rules for Determinants, Expansion of determinants in terms of rows and columns,
Adjoint formula, Cramer’s rule.
Lecture II-5(Dual Spaces): Determinant of a linear map.
Lecture II-6(Determinants and Volumes): Orientations and Volumes.
Instructor : Prof. S.A. Katre(SAK), Department of Mathematics, University of Pune, Pune-400007(sakatre at
Tutor : TBA

Module III (Linear Operators)
Lecture III-1(Polynomial algebras): Polynomials over a field, Division with remainder, Prime polynomials, Euclid’s lemma, Uniqueness of prime decomposition, Zeroes of polynomials, Prime polynomials in Q[X], R[X] and in C[X].Eisenstein irreducibility criterion.
Lecture III-2(Characteristic polynomial and minimal polynomial): Eigen-values, Spectrum, Characteristic polynomial, Cayley Hamilton theorem, Companion matrices, Invariant subspaces.
Lecture III-3(Diagonalizable and Triangulable operators): Eigenspaces, Algebraic and geometric multiplicities, Characterization of diagonalizable and triangulable operators.
Lecture III-4(Some decomposition Theorems): Primary decomposition theorem, Additive and multiplicative canonical decompositions.
Lecture III-5(The Jordan Normal forms): Jordan Normal forms
Lecture III-6(Applications): System of linear differential equations with constant coefficients.
Instructor : Prof. S.R. Ghorpade(SRG), Department of Mathematics, IIT Bombay-400076 (srg at
Tutor: TBA

Module IV (Sesqui-linear forms)
Lecture IV-1(Bilinear and Sesqui-linear forms):Sesqui-linear functions, Gram’s matrix and Gram; criterion.
Lecture IV-2(Duality and Orthogonalisation): Non-degeneracy and complete duality, Symmetric and Complex Hermitian forms, Schmidt’s orthogonalisation. .
Lecture IV-3(Types of hermitian forms): Sylvester’s Law of inertia and Hurwitz’s criterion.
Lecture IV-4(Vector spaces with scalar products): Scalar products, Cauchy-Schwartz inequality, Minkowski’s inequality,Orthogonal
projections, Bassel’s inequality, Vector products, Volumes in Euclidean spaces, Volume of the paralleotops.
Lecture IV-5(Isometries): Linear isometry and affine isometries, Rigid motions, especially of R2 and R3 .
Lecture IV-6(The Spectral Theorems): Self-adjoint and Normal operators, Principal axis theorem.
Instructor : Prof. D.P. Patil(DPP), Department of Mathematics, Indian Institute of Science,Bangalore-560012(patil at
Tutor: TBA

1. Artin,M.:Algebra, Prentice Hall, 1994.
2. Halmos,P.R.:Finite-Dimensional Vector Spaces, Springer-Verlag, 1993.
3. Herstein,I.N.:Topics in Algebra, Wiley Eastern, 1987.
4. Hoffman,K. and Kunze,R.:Linear Algebra, Prentice-Hall, 1972.
5. Jacobson,N.:Basic Algebra, Vols I and II, Hindustan Pub.Co.,1984.
6. Greub,W.:Linear Algebra, Springer-Verlag, GTM 97,(4th ed.), 1981.

Tentative Time-table

Date 9.30-11.00  11.30-13.00  14.30-15.30  16.00-17.00
17/3/14 JKV SAK T1 T2
18/3/14 JKV SAK T3 T4
19/3/14 JKV SAK T5 T6
20/3/14 JKV SAK T7 T8
21/3/14 JKV SAK T9 T10
22/3/14 JKV SAK T11 T12
24/3/14 SRG DPP T13 T14
25/3/14 SRG DPP T15 T16
26/3/14 SRG DPP T17 T18
27/3/14 SRG DPP T19 T20
28/3/14 SRG DPP T21 T22
29/3/14 SRG DPP T23 T24

Tn— nth tutorial
Tea Breaks—11.00-11.30 and 15.30-16.00
Lunch Break— 13.00 - 14.30

Selected Applicants

(Go through the list carefully and then write to me (if you have any querry))

Sr SID Ful Name Gender 1st Step Status
of hard copy received
(R) /not received(NR) at CEMS
2nd Step
3rd Step
1 4891 Dr. Amit K. K Awasthi Male R Confirmed Not coming
2 4901 Mr Amrinder Pal Singh Male NR Not coming ---
3 4909 Dr. Bibhas Chandra Saha Male R Confirmed Confirmed
4 4931 Dr. Rakesh Kumar Bajaj Male R Confirmed Not coming
5 4944 Mr. Faroz Ahmad Bhat Male R Confirmed Confirmed
6 4950 Mr. Hrishikesh Vidyadhar Khaladkar Male R Not coming ---
7 4955 Mr. Sunil Dattu Howal Male R Not coming ---
8 4956 Dr. Shery  Fernandez Male R Confirmed Confirmed
9 4957 Mr. Ram  Kishor Male R Not coming ---
10 4961 Mr. Edwin  Tomson Male R Confirmed Confirmed
11 4968 Dr. Harish  Chandra Male R Confirmed Confirmed
12 4972 Dr. Harpreet  Kaur Female R Confirmed Confirmed
13 4975 Dr. Juthika  Mahanta Female NR Not coming ---
14 4996 Mr. Gobinda Chandra Panda Male R Confirmed Confirmed
15 5003 Mr. Vishal  Gupta Male R Confirmed Confirmed
16 5033 Mr Prithwiraj  Halder Male R Confirmed Confirmed
17 5034 Mr. Sharad Bhagwanrao Kadam Male NR Not coming ---
18 5039 Dr Ashok Kumar Goli Male R Confirmed Confirmed
19 5073 Dr Sharan  Jeet Female NR Not coming ---
20 5081 Mr. Virivinti  Kiran Male NR Not coming ---
21 5097 Mr. Pawan  Tamta Male R Confirmed Confirmed
22 5110 Dr. Dhananjoy  Mandal Male R Confirmed Confirmed
23 5111 Dr. Hemlata  Pande Female R Confirmed Confirmed
24 5112 Ms Jita  Parida Female R Confirmed Confirmed
25 5118 Mr. Gurusamy  Rajendran Male NR/will be sent by 25th Not coming ---
26 5119 Mr. Durai Baskar  Arunachalam Male NR Not coming ---
27 5123 Mr. D.Durga  Prasad Male R Confirmed Confirmed
28 5139 Mr. Dilip  Jain Male NR/send scanned copy by 25th Confirmed Not coming
29 5141 Dr. Amarpreet  Kaur Female NR Not coming ---
30 5160 Mr. Girish Chandra Nayak Male NR Not coming ---
31 5174 Dr. Sunil Kumar Chanyal Male R  Confirmed  Confirmed
32 5189 Dr Nagaiah  Thandu Male R  Confirmed  Confirmed
33 4893 Dr. Khushwant Singh Chahal Male R  Confirmed  Confirmed
34 4895 Mr. Suhail Gulzar Mattoo Male R Confirmed   Confirmed
35 4896 Mr. Sajad Hussain Ahangar Male R  Confirmed  Confirmed
36 4917 Mr. Irshad Ahmad Sheikh Male R Confirmed   Confirmed
37 4959 Ms. Dilpreet  Kaur Female R Confirmed   Confirmed
38 5024 Ms Jayeeta  Saha Female R Confirmed  Confirmed
39 5025 Mr. Bipul  Pal Male R Confirmed   Confirmed
40 5027 Dr. Sudip Kumar Pal Male R  Not coming ---
41 5099 Mr. Prabakaran  P Male R Confirmed  Confirmed 
42 5121 Ms Lubna Wali Shah Female R Confirmed  Confirmed 
43 5126 Ms Tawheeda  Rasool Female R  Confirmed Confirmed 
44 5165 Mr. Mohd  Furkan Male R Confirmed  Confirmed 
45 5178 Mr. Gagandeep  Singh Male R Confirmed  Confirmed 
Confirmation of Wait-Listed Participants
( here only those names will appear who have confirmed all 3 steps)
Sr SID Ful Name Gender 1st Step Status of
hard copy received (R)/not
received(NR) at CEMS
2nd Step
3rd Step
1 5124 Vijay Kumar Yadav Male R Confirmed  Confirmed 
2 4969 Mohit Kumar Male R Confirmed  Confirmed 
3 4970 Narottam Singh Chauhan Male R Confirmed  Confirmed 
4 5037 Laxmi Narayan Mishra Male R Confirmed  Confirmed 
5 4911 Akanksha Agrawal (F) Female R Confirmed  Confirmed 
6 5075 Sayantan Mukherjee Male R Confirmed  Confirmed 
7 4921 Bharath Kumar Ethamakula Male R Confirmed  Confirmed 
8 5022 Meenu Devi (Rathore) Female R Confirmed  Confirmed 
9 5146 Shiv Prasad   R Confirmed  Confirmed 
10 4975 Shelly Garg Female R Confirmed  Confirmed 
11 4197 Deepmala Female R Confirmed  Confirmed 
CEMS Invitees / Local participants
1   Dilip Kumar Male R Confirmed  Confirmed 
2   Sunny Manchanda Male R Confirmed  Confirmed 
3 5182 Deepa Kandpal (F) Female R Confirmed  Confirmed 
4 5183 Jyoti Rani (F) Female R Confirmed  Confirmed 

Very -Very Important:



Those who needs selection/invitation letter for leave from their institute/college/university should send mail to . Please do not forget to mention followings:

  1. Title (Dr./Mr/Ms)
  2. Name
  3. Department
  4. Address of institution where you are working with PIN-Code.


  1. In March-April Almora and surroundings are at their BEST.
                 ***It is moderately cold***
                *** It is season of flowers***
  2. In case of any querry please feel free to contact Sanjay Kumar Pant :
    Mobile: 919810528236 E-mail:
  3. For updates visit :

*** If anytime you decide that you will not come for the school , Please let us know.***

How to reach

  • Travel By Air: The nearest airport is New Delhi. From Delhi one can reach Almora by train or by road as given below.
  •  By Train: The nearest train station is Kathgodam. Several important rail stations in India have direct connection to Kathgodam. From Delhi, there three main trains run almost daily from Delhi to Kathgodam: 12040 ANVT-KGM Shatabdi (06:15 AM), 15013 Ranikhet Express (22:40) and 15035 UTR-SAMPARK Express (16:00). We recommend the first two connections. One may also get down at Haldwani (the station just before Kathgodam). Please note that train number 12040 starts from ANAND VIHAR railway station at Delhi and the other two trains depart from OLD DELHI railway station. So, if you plan to reach Kathgodam by train, after arriving at the airport or New Delhi railway station, you should direct yourself towards the Anand Vihar railway terminus or the Old Delhi rail station in Delhi. The metro stops most nearest to these rail stations are Anand Vihar and Chandni Chowk respectively.

  Summary of trains:
 *1. Delhi - Kathgodam by Ranikhet Express. (Train No. 15013)

 *2. Anand Vihar (ANVT)-Kathgodam (KGM) Shatabdi (Train o. 12040)

   3. Delhi - Kathgodam by Uttarakhand Smprk Kranti Express (Train No.15035)

   4. Delhi - Lal Kuan by Pooja Express. (Train No. 0517)

Trains with asterix are recommended.

  •  By Road: This option is little expensive, but direct and in many cases, would be flexible. This option is to travel to Almora from New Delhi Airport by road. You can book a (private) taxi at the airport or in advance. By car it generally takes 8-10 hours to Almora (from Delhi airport) assuming that you will take one or two breaks in between the journey.

    AC Volvo buses are also available from ISBT Delhi to Kathgodam.

  • Car Direction: Delhi - Hapur bypass - Moradabad bypass - Rampur - Bilaspur - Rudrapur - Haldwani - Kathgodam [approximately 270 kms]- Ranibagh - Bhimtal - Bhowali - Khairna Bridge - Kwarah Bridge - Almora. From Kathgodam/Haldwani to Almora: One has to travel this route by car or bus. It takes sround 3 hrs to reach Almora from Kathgodam. We recommend you to hire a car or shared taxi at Kathgodam/Haldwani. If you intend to travel by a shared taxi, it is better to get down at Haldwani since the availability of shared taxis are better there. On the way to Almora from Kathgodam/Haldwani, you will have to cross some beautiful tourist locations, for example, Bheemtal (

Link to School site