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#### Linear Algebra (Code-09050602)SYLLABUS

 S.No. Contents Domain Time Hour 1 Vector Spaces Subspaces, sum and direct sum of subspaces Linear span Linearly dependent and independent subsets of vector space Finitely generated vector space &Existence theorem for  basis of a finitely generated vector space Finite dimensional vector spaces Invariance of no. of elements of basis set, Dimensions Quotient space and its dimension Must know 12 2 Homomorphism and isomorphism of vector spaces Linear transformations and linear  form of vector spaces Vector spaces of all the linear transformations Dual spaces, Bi-dual spaces Annihilator of subspaces of finite dimensional vector spaces Null space, Range space of a linear transformation, Rank & Nullity theorem Algebra of linear transformations Minimal polynomial of linear transformation Singular & Non –Singular linear transformation Matrix of a linear transformation Change of basis Eigen values and Eigen vector of linear transformations Must know 14 3 Algebra of linear transformations Minimal polynomial of linear transformation Singular & Non –Singular linear transformation Matrix of a linear transformation Change of basis Eigen values and Eigen vector of linear transformations Must know 8 4 Inner product spaces Cauchy Schwarz inequality Orthogonal vectors, orthogonal complements Orthogonal sets and basis Bessel’s inequality for finite dimensional vector spaces Gram-Schmidt Orthogonalization process Adjoint of a linear transformation and its properties Unitary Linear Transformations Nice to know 10

Books Recommended:

• I.N. Herstein: topics in Algebra, Wiley Eastern Ltd., New Delhi, 1975
• Vivek Sahai and Vikas Bist: Algebra, Narosa Publishing House
• I.S. Luther and I.B.S. Passi: Algebra, Vol-II, Narosa Publishing House.
• P.B. Bhattacharya, S.K. Jain and S.R. Nagpal: Basic Abstract Algebra(2nd edition).
• Gilbert Strang: Linear Algebra and its applications, Thomson 2007
• S. Kumarsen: Linear Algebra-A Geometric Approach, Prentic Hall of India Pvt. Ltd.,1999.
• Kenneth Hoffman, Ray Alden Kunze: Linear Algebra, 2nd Ed., Prentic Hall of India Pvt. Ltd., 1971.