MA 4020: Linear Algebra
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Class timings:
XXday: XX:XX XX to XX:XX XX
XXday: XX:XX XX to XX:XX XX
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.
- 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.