Course Archives Theoretical Statistics and Mathematics Unit | ||||||||
Course: Linear Algebra I Level: Undergraduate Time: Currently not offered |
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Syllabus Past Exams Syllabus: Homogeneous and non-homogeneous systems of linear equations, condition for consistency, solution set as a translate of a subspace. Vector spaces, subspaces, linear independence, span, basis and dimension, sum and intersection of subspaces, direct sum, complement and projection. Linear transformation and its matrix with respect to a pair of bases, properties of matrix operations, use of partitioned matrices. Column space and row space, rank of a matrix, nullity, rank of AA*. g-inverse and its elementary properties, left inverse, right inverse and inverse, inverse of a partitioned matrix, lower and upper bounds for rank of a product, rankfactorization of a matrix, rank of a sum. Elementary operations and elementary matrices, Echelon form, Normal form, Hermite canonical form and their use in solving linear equations and in finding inverse or g-inverse. LDU-decomposition. Note: The field of scalars should be assumed to be subfields of complex numbers, i.e., subsets closed under addition, subtraction, multiplication and division by a nonzero number. The main examples to be considered should be the field of real, complex or rational numbers. Reference Texts: (a) C. R. Rao: Linear Statistical Inference and its Applications. (b) A. Ramachandra Rao and P. Bhimasankaram: Linear Algebra. (c) K. Hoffman and R. Kunze: Linear Algebra. (d) F. E. Hohn: Elementary Matrix Algebra. (e) P. R. Halmos: Finite Dimensional Vector Spaces. (f) S. Axler: Linear Algebra Done Right! (g) H. Helson: Linear Algebra. (h) R Bapat: Linear Algebra and Linear Models. (i) R. A. Horn and C. R. Johnson: Matrix Analysis. (j) M. Artin: Algebra. Evaluation:
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