M205: Linear Algebra
Syllabus:
- System of Linear equations
- Matrices and elementary row operations, Reduced echolen form of
matrices
- Vector spaces, Subspaces, Quotient spaces
- Bases and dimension
- Direct sums
- Linear transformations and their matrix representations
- Dual vector spaces, Transpose of a linear transformation
- Polynomial rings over a field
- Determinant and their properties
- Eigenvalues and eigenvectors
- Characterstic polynomial and minimal polynomial
- Triangulation and diagonalization
- Direct sum decompositions
- Primary decomposition theorem
References:
- Linear Algebra: K. Hoffman and R. Kunze, Prentice
Hall India
- Finite dimensional Vector spaces: Halmos, Springer
- Introduction to Linear Algebra, S. Lang, Springre
- Algebra: M. Artin, Prentice Hall India
- Topics in Algebra, I. N. Herstein, Wiley India
Lectures:
- Monday [T] (9.30--10.30)
- Tuesday (10.30--11.30)
- Wednesday (11.30--12.30)
- Thursday (13.30--14.30)
Assignment:
- Assignment 1
- Assignment 2
- Assignment 3
- Assignment 4
- Assignment 5
- Assignment 6
Quiz:
Examination:
- Mid- Semester
- End- Semester
Evaluation Procedure for Grading:
There will be three quizzes carrying 10
marks each, a mid-semester examination of 30 marks and one
final end-Semester exam of 40 marks (Total 100). The final grading will
be done based on the performance in the quizzes, mid-semester and
end-semester examination. Suppose the total marks obtained by
a student is x out of 100. Then the grading will be as
follows:
- 0<=x< 30---FR
- 30<=x<40---DD
- 40<=x<50---CD
- 50<=x<60---CC
- 60<=x<70---BC
- 70<=x<80---BB
- 80<=x<90---AB
- 90<=x<=100---AA
Keys to Success:
Attend all the lectures and tutorials, Do the homeworks, ask
questions. Talk to me if you have any problem.