MA 4020: Linear Algebra
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Class timings:
Monday: 10:00 am to 10:55 am
Wednesday: 09:00 am to 09:55 am
Thursday: 11:00 am to 11:55 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 Row Operations, Row-Reduced Echelon Matrices, Gaussian Elimination. Vector Spaces, Subspaces, Direct Sums, Bases and Dimension, Linear Transformations,
Kernals, Range Space, Rank-Nullity Theorem, The Matrix of a Linear Transformations, Invertibility, Determinants, Linear Functionals and Adjoints.
Eigenvalues and Eigenvectors, Cayley-Hamilton Theorem, Invariant Subspaces, Upper-Triangular Matrices, Diagonal Matrices. The Minimal Polynomial,
Diagonalizability, algebraic, geomentric multiplicities, Generalized Eigenvectors, Rational Canonical forms, Jordan Canonical Forms.
Inner Products, Norms, Orthonormal Bases, Gram-Schmidt process, Schur's theorem, Orthogonal Projections and Minimization Problems,
Self-Adjoint and Normal Operators, The Spectral Theorem for finite dimensional operators.
References:
- K. Hoffman and R. Kunze, Linear Algebra, PHI Learning, Second Edition, 2009.
- A. Ramachandra Rao, P. Bhimasankaram, Linear Algebra, TRIM Series, 2000.
- Dummitt, D.S. and Foote, R.M. (2004) Abstract Algebra. 3rd Edition, John Wiley & Sons, Inc.
- Jacobson, Nathan. Basic algebra. I. Second edition. W. H. Freeman and Company, New York, 1985.