MA 4020: Linear Algebra
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Class timings:
Tuesday: 4:00 pm to 5:25 pm
Friday: 2:30 pm to 3:55 pm
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.