IST - Advanced Linear Algebra (2023)

Speakers and Syllabus

Syllabus:

Sr. Name of the speaker and Affiliation
 Topic of lectures Number of lectures
1 Dr. Supriya Pisolkar
IISER, Pune

Canonical Forms.

  • Eigenvalues and eigenvectors of matrices and linear maps, Diagonalizability.
  • Minimal and characteristic polynomials, Cayley-Hamilton theorem.
  • Jordan and Rational canonical forms over complex numbers.
  
2 Prof. Vinayak Sholapurkar
S.P. College, Pune/ Bhaskaracharya Pratishthana, Pune.		 Inner products and Orthogonality. 
  • Bilinear forms, Symmetric bilinear forms, hermitian forms.
  • Orthogonality, Orthonormal basis, Gram-Schmidt process.
  • Spectral theorem.
  • Basic theory of inner products on real and complex vector spaces.
  • Spectral theorem for hermitian and normal linear maps (finite dimensional case).
  
3 Dr. Chandrasheel Bhagwat  Multilinear Algebra.  
  • Multilinear maps on vector spaces: basic theory and examples.
  • Theory of determinant map as an alternating n-linear form on F^n.
  • Tensor product of vector spaces, symmetric tensors, alternating tensors.
  • Applications to differential forms on euclidean spaces and deRham cohomology.
  
4 Prof. B. Sury
ISI Bangalore		  Quadratic forms and Linear groups.  
  • Quadratic forms: Classification, signature for real quadratic forms.
  • Linear Groups defined preserving quadratic forms: Orthogonal and Unitary groups.
  • Groups SO (3) and SU (2), conjugacy classes and geometry of sphere. 
  

References:

  1. M. Artin, Algebra, Pearson Publications.
  2. Hoffman and Kunze, Linear Algebra, Pearson publications.

Course Associates

  •  Mr. Gahininath Sonawane, S. P. College, Pune.
  •  Dr. Aman Jhinga
  •  Mr. Mandar Khasnis
  •  Mr. Shubham Jaiswal, IISER, Pune.  

 

 Special lecture by  Prof. Dipendra Prasad  Saturday, 9th December 2023.

Time Table

 

 

Monday

27/11/23

Tuesday

28/11/23

Wednesday

29/11/23

Thursday

30/11/23

Friday

1/12/23

Saturday

2/12/23

9:30 – 11:00

SP

SP

SP

SP

SP

SP

11:00 –11:30

TEA BREAK

11:30 – 1:00

VS

VS

VS

VS

VS

VS

1:00 – 2:30

LUNCH BREAK

2:30 – 3:30

VS/AJ/SJ

VS/AJ/GS

VS/AJ/GS

VS/AJ/GS

VS/AJ/GS

VS/AJ/GS

3:30 – 4:00

TEA BREAK

4:00 – 5:00

SP/AJ/SJ

SP/AJ/SJ

SP/AJ/SJ

SP/AJ/SJ

SP/AJ/SJ

SP/AJ/SJ

5:00 – 5:30

SNACKS

 

 

Monday

4/12/23

Tuesday

5/12/23

Wednesday

6/12/23

Thursday

7/12/23

Friday

8/12/23

Saturday 9/12/23

9:30 – 11:00

CB

CB

CB

CB

CB

CB

11:00 –11:30

TEA BREAK

11:30 – 1:00

BS

BS

BS

BS

BS

BS

1:00 – 2:30

LUNCH BREAK

2:30 – 3:30

CB/MK/GS

CB/MK/SJ

CB/MK/GS

CB/MK/GS

CB/MK/GS

SL

3:30 – 4:00

TEA BREAK

4:00 – 5:00

BS/MK/SJ

BS/MK/SJ

BS/MK/SJ

BS/MK/SJ

BS/MK/GS

SL

5:00 – 5:30

SNACKS

Abbreviation with name of the speaker

Resource persons:

SP: Supriya Pisolkar
VS: Vinayak Sholapurkar
BS: B. Sury
CB: Chandrasheel Bhagwat

 

Course associates:
AJ: Aman Jhinga
SJ: Shubham Jaiswal
GS: G.L.Sonawane
MK: Mandar Khasnis

SL: Special lecture slot.

 

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