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 : 5:30-6:00 in LH-4
2. Projesh Nath (You are assigned to him if your S.R No's last digit is odd) : Tutorial on Wednesdays : 5:30-6:00 in LH-3
Classroom and timings : Tuesdays and Thursdays from 2:00-3:30 in LH-4.
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. , Midterm-35%, and
50% for the Final.
Exams :
The Midterm shall be held on 26 Sept from 2-3:30 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 Nullity-Rank 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 2-4) |
|
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 Cayley-Hamilton 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 Grahm-Schmidt process and Cholesky decomposition (Thursday notes) |
|
15 |
4 Nov - 10 Nov |
Orthogonal projections, Finite-dimensional 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 self-adjoint operators on finite-dimensional spaces (Thursday notes) |
|
17 |
18 Nov - 24 Nov |
The spectral theorem for Normal operators, Sylvester's law of inertia (Tuesday notes); Positive-definiteness 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 |