Course Archives Theoretical Statistics and Mathematics Unit
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Course: Linear Algebra Instructor: Manish Kumar Room: G25 Time: Currently offered Level: Postgraduate |
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Syllabus Past Exams Syllabus: 1. Review of linear transformations and matrices. Eigenvectors, characteristic polynomial, orthogonal matrices and rotations. Inner product spaces, Hermitian, unitary and normal transformations, spectral theorems, bilinear and quadratic forms. Multilinear forms, wedge and alternating forms.2. Review of basic concepts from rings and ideals required for module theory (if necessary). Modules over commutative rings: examples. Basic concepts: submodules, quotients modules, homomorphisms, isomorphism theorems, generators, annihiliators, torsion, direct product and sum, direct summand, free modules, finitely generated modules, exact and split exact sequences. Time permitting: snakes lemma, complexes and homology sequences. 3. Properties of K[X] over a field K. Structure theorem for finitely generated modules over a PID; applications to Abelian groups, rational and/or Jordan canonical forms. Suggested Texts:1. D.S. Dummit and R.M. Foote, Abstract Algebra, John Wiley (Asian reprint 2003). 2. S. Lang, Algebra, GTM (211), Springer (Indian reprint 2002). 3. K. Hoffman and R. Kunze, Linear Algebra, Prentice-Hall of India (1998). 4. N.S. Gopalakrishnan, University Algebra, Wiley Eastern (1986). Evaluation:
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Midterm
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Solution
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