Details of MA2101 (Autumn 2012)

Level: 2 Type: Theory Credits: 3.0

Course CodeCourse NameInstructor(s)
MA2101 Linear Algebra Satyaki Mazumder

Syllabus
MA2101 Linear Algebra (3 Credits)

Vector Spaces: Definition of a vector space, examples; linear independence, basis and dimension; scalar product, orthogonal basis and the Gram-Schmidt orthogonalization process.

Linear Operators and Matrices: Definition, matrix representation of linear operators, notions of rank and kernel; change of basis, similarity, orthogonal matrices.

Determinants: Determinant of a matrix, geometric interpretation of the determinant, determinant and non-singularity.

System of Linear Equations: Solvability of linear equations, general description of the solution set, geometric interpretation; methods to solve linear equations, Cramers rule, Gaussian elimination.

Eigenvalues and Eigenvectors: Eigenvalues and eigenvectors of a matrix, the characteristic polynomial, Cayley-Hamilton Theorem; diagonalization, orthogonal diagonalizability of symmetric matrices, Principal Axes Theorem and its connection with co-ordinate geometry; Jordan canonical form.



References
Suggested Texts / Reference Books:

1. Axler, S., Linear Algebra Done Right (2nd Edition), Undergraduate Texts in Mathematics, Springer-Verlag, 1997.

2. Horn, R. and Johnson, C. R., Matrix Analysis, Cambridge University Press, 1985.

3. Hoffman, K. and Kunze, R., Linear Algebra (2nd Edition), Prentice-Hall, 1971.

4. Lang, S., Introduction to Linear Algebra (2nd Edition), Springer-Verlag, 1997.

5. Rao, A. R. and Bhimasankaram, P., Linear Algebra (2nd Edition), Texts and Readings in Mathematics, Hindustan Book Agency, 2000.


Course Credit Options

Sl. No.ProgrammeSemester NoCourse Choice
1 IP 1 Not Allowed
2 IP 3 Not Allowed
3 MS 3 Not Allowed
4 RS 1 Not Allowed