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

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