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This is a graduate course on linear algebra. I will be covering the first six
chapters of the book Linear Algebra by Friedberg, Insel and Spence.
Along the course I will indicate some of the applications but we will not be
studying them in great detail. The lecture schedule and contents of a previous
offering of this course is available here

Textbook: Linear Algebra, 4th Ed. by Friedberg, Insel and Spence

Course topics.

- Vector spaces
- Linear transformations
- Systems of linear equations
- Determinants
- Eigenvalues, eigenvectors
- Inner product spaces
- Additional topics (time permitting)

Grading policy (Tentative)

5% Homework+scribing, 5% Miniquizzes, Project 10%, 30% Mid sem, 50% End sem.

Exam schedule

Midsem 24/25th Sep (Tentative)

Endsem 24th Nov (as per Institute schedule)

LaTeX files for scribing

lecture-xy-keyword.tex and xy.tex. Sample output looks like
this

Naming convention: For lecture number xy use lecture-xy-keyword.tex (just use one key word from the title) as the main file and let the entire scribe notes be in the file xy.tex. Number lectures as below.
If the latex commands/packages are not sufficient, then add them in the preamble of lecture-xy-keyword.tex

Lectures

- 30 Jul Lecture 01: Introduction

- 06 Aug Lecture 02: Vector spaces

- 07 Aug Lecture 03: Subspaces

- 13 Aug Lecture 04: Linear (in)dependence and bases

- 14 Aug Lecture 05: Bases - further properties

- 20 Aug Tutorial-1 (vector spaces)

- 21 Aug Lecture 06: Linear transformations, Miniquiz- 1

- 27 Aug Lecture 07: Linear transformations - further properties

- 28 Aug Lecture 08: Matrix representations and invertible transformations

- 29 Aug Lecture 09: Invertible transformations

- 30 Aug Tutorial-1 (vector spaces)

- 03 Sep Lecture 10: Systems of linear equations

- 04 Sep Tutorial-2 (linear transformations)

- 05 Sep Lecture 11: Rank of a matrix

- 10 Sep Lecture 12: Solving systems of linear equations

- 11 Sep Tutorial-3

- 12 Sep Lecture 13: Systems of linear equations-wrapup

- 17 Sep Lecture 14: Determinants

- 18 Sep Lecture 15: Determinants

- 19 Sep Lecture 16: Review

- 24 Sep Midsem

- 25 Sep Tutorial-4

- 01 Oct Lecture 17: Eigenvalues, eigenvectors

- 03 Oct Lecture 18: Eigenvalues, eigenvectors

- 08 Oct Lecture 19: Diagonalizability and Cayley-Hamilton theorem

- 09 Oct Lecture 20: Cayley-Hamilton theorem

- 10 Oct Tutorial-5

- 15 Oct Lecture 21: Inner products and norms

- 16 Oct Lecture 22: Orthogonality and miniquiz-4

- 17 Oct Lecture 23: Orthogonal complements

- 22 Oct Lecture 24: Adjoint of an operator

- 23 Oct Lecture 25: Least squares approximation

- 24 Oct Lecture 26: Normal operators and miniquiz-5

- 29 Oct Lecture 27: Self-adjoint and unitary operators

- 31 Oct Lecture 28: Orthgonal projections and spectral theorem

- 05 Nov Lecture 29: Spectral theorem and equivalence of matrices

- 07 Nov Lecture 30: SVD

- 08 Nov Lecture 31: SVD and pseudoinverse

- 12 Nov Tutorial-6

- 13 Nov Tutorial and miniquiz-6

- 27 Nov Endsem