MA 219 (Linear Algebra) - Autumn 2019 - Vamsi Pingali


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 TBA. (Syllabus : TBA)

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)

14

28 Oct - 3 Nov

15

4 Nov - 10 Nov

16

11 Nov - 17 Nov

17

18 Nov - 24 Nov



How's the HW ? Sigh....sir....

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

HW 1

7

11 Sept

HW 2

8

18 Sept (Note this !!!)

HW 3

11

9 Oct

HW 4

13

23 Oct

HW 5