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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.
If there is time some additional topics will be covered.

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)

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

Lectures

- 30 Jul Introduction

- 01 Aug Vector spaces, subspaces

- 04 Aug Subspaces, linear combinations

- 05 Aug Linear dependance and linear independence

- 06 Aug Bases of vector spaces

- 08 Aug Further properties of bases

- 11 Aug Tutorial

- 12 Aug No class

- 13 Aug Replacement theorem and consequences

- 18 Aug Tutorial

- 19 Aug Tutorial

- 20 Aug No class

- 21 Aug Makeup class (Dr. Arun Pachai) : Linear transformations

- 22 Aug Makeup class (Dr. Arun Pachai) : Linear transformations

- 25 Aug No class

- 26 Aug No class

- 27 Aug No class

- 28 Aug Makeup class (Dr. Arun Pachai) : Linear transformations

- 01 Sep Composition of linear transformations

- 02 Sep Linear tranformations & matrices

- 03 Sep Invertible linear transformations, isomorphisms, Miniquiz-2

- 05 Sep Invertible linear transformations, isomorphisms

- 08 Sep Change of basis, dual vector spaces

- 09 Sep Systems of linear equations-basics

- 10 Sep Miniquiz-3, Rank of matrix

- 12 Sep Properties of matrix rank

- 15 Sep Tutorial-3

- 16 Sep Systems of linear equations

- 17 Sep Discussion Miniquiz-3, Miniquiz-4

- 19 Sep Linear systems of linear equations-wrapup

- 22 Sep Determinants

- 23 Sep Tutorial on linear systems of equations

- 24 Sep Eigenvalues and eigenvectors

- 25 Sep Tutorial (Extra class)

- 26 Sep Eigenvalues and eigenvectors, diagonalization

- 29 Sep Midsemester examination

- 30 Sep Further properties of eigenvalues, eigenvectors

- 01 Oct Conditions for diagonalization; Application: Google's pagerank algorithm

- 07 Oct PageRank algorithm

- 08 Oct PageRank algorithm wrapup and midsem paper discussion

- 10 Oct Invariant subspaces and Cayley-Hamilton Theorem

- 13 Oct Cayley Hamilton Theorem

- 14 Oct Wrapup on diagonalization, problem session

- 15 Oct Tutorial, miniquiz-5

- 17 Oct Inner products

- 20 Oct Inner products, norms

- 21 Oct Gram-Schmidt orthogonalization

- 24 Oct Orthogonalization, and orthogonal complements, miniquiz-6

- 27 Oct Orthogonal complements and projectors

- 28 Oct Adjoint of an operator

- 29 Oct Least squares solution

- 31 Oct Normal operators

- 03 Nov Normal and self-adjoint operators

- 05 Nov Unitary and orthogonal operators

- 07 Nov Tutorial and miniquiz-7

- 10 Nov Orthogonal projections and Spectral theorem

- 11 Nov Spectral theorem, wrapup

- 21 Nov End semester exam