Details of MA2101 (Autumn 2012)
Level: 2 | Type: Theory | Credits: 3.0 |
Course Code | Course Name | Instructor(s) |
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MA2101 | Linear Algebra | Satyaki Mazumder |
Syllabus |
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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 |
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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. | Programme | Semester No | Course Choice |
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1 | IP | 1 | Not Allowed |
2 | IP | 3 | Not Allowed |
3 | MS | 3 | Not Allowed |
4 | RS | 1 | Not Allowed |