The text we will (largely) be following is "Linear Algebra" by Hoffman and Kunze. We will try to cover as much of this book as possible. Here are some other references :
1. M. Artin, Algebra.
2. S. Lang, Linear Algebra.
3. G. Strang, Linear algebra and its applications.
Instructor :
Vamsi Pritham Pingali, vamsipingali@iisc.ac.in.
Office : N23 in the mathematics building.
Teaching Assistants :
1. GVK Teja (You are assigned to him if your S.R No's last digit is even) : Tutorial on Wednesdays : 5:306:00 in LH4
2. Projesh Nath (You are assigned to him if your S.R No's last digit is odd) : Tutorial on Wednesdays : 5:306:00 in LH3
Classroom and timings : Tuesdays and Thursdays from 2:003:30 in LH4.
The Grading policy : 15% for Quizzes  One quiz every fortnight to be held during the tutorial session. It will contain a couple of problems from the HW. , Midterm35%, and
50% for the Final.
Exams :
The Midterm shall be held on 26 Sept from 23:30 in our usual classroom. (Syllabus : Everything upto and including Adjoints (That is upto and including Week 8))
The final for this course will be held on Wednesday, Dec 4th from 2:00 pm to 5:00 in our usual classroom. (Syllabus : Everything done in the class except the last two applications (least squares and PCA).)
Ethics: Read the information on the
IISc student ethics page. In short, cheating is a silly thing. Don't do
it.
Here
is the tentative schedule. (It is subject to changes and hence
visiting this webpage regularly is one of the best ideas in the
history of best ideas.)
Wk 
Dates 
Syllabus covered 
1 
29 July  4 Aug 
Logistics, motivation, definition of fields, elementary row operations (Thursday notes) 
2 
5 Aug  11 Aug 
Row echelon form, matrix multiplication (Tuesday notes); Invertibility, Definition of Vector spaces (Thursday notes) 
3 
12 Aug  18 Aug 
Vector spaces, subspaces (Tuesday notes); Thursday was a holiday 
4 
19 Aug  25 Aug 
Basis and dimension (Tuesday notes); Extending bases (Thursday notes) 
5 
26 Aug  1 Sept 
Change of basis, definitions of row and column ranks (Tuesday notes); Linear transformations and the NullityRank theorem (Thursday notes) 
6 
2 Sept  8 Sept 
Quotient spaces, L(V,W) (Tuesday notes),; Change of basis (Thursday notes) 
7 
9 Sept  15 Sept 
Tuesday was a holiday; Dual spaces (Thursday notes) 
8 
16 Sept  22 Sept 
Double dual, Adjoint (Tuesday notes), Tensor products (Thursday notes) 
9 
23 Sept  29 Sept 
Midterm week (our midterm is on 26 Sept from 24) 
10 
30 Sept  6 Oct 
Determinants (Tuesday notes), (Thursday notes) 
11 
7 Oct  13 Oct 
Tuesday was a holiday; Eigenvalues and eigenvectors  definitions and examples (Thursday notes) 
12 
14 Oct  20 Oct 
The CayleyHamilton theorem (Tuesday notes); The minimal polynomial (Thursday notes) 
13 
21 Oct  27 Oct 
Generalised Eigenvalues and Eigenvectors (Tuesday notes); Jordan Canonical Form (Thursday notes) 
14 
28 Oct  3 Nov 
Inner products and norms (Tuesday notes); Uncertaintly principle, the GrahmSchmidt process and Cholesky decomposition (Thursday notes) 
15 
4 Nov  10 Nov 
Orthogonal projections, Finitedimensional little Riesz representation theorem (Tuesday notes); Norms of operators, Unitary operators (Thursday notes) 
16 
11 Nov  17 Nov 
Tuesday was a holiday; The spectral theorem for selfadjoint operators on finitedimensional spaces (Thursday notes) 
17 
18 Nov  24 Nov 
The spectral theorem for Normal operators, Sylvester's law of inertia (Tuesday notes); Positivedefiniteness through minors, least squares, PCA (Thursday notes) 
Wk 
Week 
Quiz to be held on (subject to changes; please check regularly) 
1 
29 July  4 Aug 
No HW/Quiz 
2 
5 Aug  11 
No HW/Quiz 
5 
28 Aug 

7 
11 Sept 

8 
18 Sept (Note this !!!) 

11 
9 Oct 

13 
23 Oct 

15 
6 Nov 

17 
20 Nov 