MA 4020: Linear Algebra

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### Class timings:

Monday: 9:00 am to 9:55 am

Wednesday: 11:00 am to 11:55 am

Thursday: 10:00 am to 10:55 am

### Examination and Grades:

The grades will be decided by the marks obtained in the assignments, mid-term, surprise tests, the final examination, and also by the performance in the class.

## Syllabus:

System of Linear Equations, Elementary Operations, Row-Reduced Echelon Matrices, Gaussian Elimination. Vector Spaces, Subspaces, Direct Sums, Bases and Dimension, Linear Maps, Rank-
Nullity Theorem, The Matrix of a Linear Map, Invertibility. Eigenvalues and Eigenvectors, Invariant Subspaces, Upper-Triangular Matrices, Diagonal Matrices.

Inner Products, Norms, Orthonormal Bases, Gram-Schmidt process, Schur's theorem, Orthogonal Projections and Minimization Problems, Linear Functionals and Adjoints.
Self-Adjoint and Normal Operators, The Spectral Theorem for finite dimensional operators. Generalized Eigenvectors, The Characteristic Theorem, The Minimal Polynomial, Jordan Form.
Polynomial, Cayley-Hamilton Theorem, The Minimal Polynomial, Jordan Form.
## References:

- K. Hoffman and R. Kunze, Linear Algebra, PHI Learning, Second Edition, 2009.
- A. Ramachandra Rao, P. Bhimasankaram, Linear Algebra, TRIM Series, 2000.
- Sheldon Axler, Linear Algebra Done Right, University Press, 2010.
- Friedberg H. Stephen, Insel J. Arnold, Spence E. Lawrence, Linear Algebra, PHI Learning, Fourth Edition 2009.

## Assignments:

The assignments have to be submitted right after the class on the respective due dates. The assignments can be submitted after the due date and time as well,
but only 50% of the marks will be credited into your account, unless you have a valid reason for the late submission. Assignments have to be submitted in A4 white sheets.