Details of MA2102 (Autumn 2016)

Level: 2 Type: Theory Credits: 3.0

Course CodeCourse NameInstructor(s)
MA2102 Linear Algebra Shibananda Biswas

MA2102 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: Definition, matrix representation of linear operators, rank of a matrix, determinants, nonsingularity, partitioned matrices, special types of matrices; change of basis.

Eigenvalues and Eigenvectors: Eigenvalues and eigenvectors of a matrix, the characteristic polynomial, diagonalization.

Similarity: Orthogonal, unitary and Hermitian matrices, unitary similarity, Schur's triangularization theorem, the spectral theorem for normal matrices; the QR algorithm; the Hermite normal form, the Jordan canonical form and the minimal polynomial.

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 IP 5 Not Allowed
4 MR 1 Not Allowed
5 MR 3 Not Allowed
6 MS 3 Core
7 RS 1 Not Allowed
8 RS 2 Not Allowed