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

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

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