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### Title-Linear Algebra (Code-09010602)

 S.No Unit Contents Learning Objective Teaching Guidelines Methodology Time (Hrs) 1 One 1. Vector Spaces, Subspaces, sum and direct sum of subspaces, Linear span 2. Linearly dependent and independent 3. Finitely generated vector space &Existence theorem 4. Finite dimensional vector spaces 5. Invariance of no. of elements of basis set, Dimensions 6. Quotient space and its dimension To study Vector Spaces, its subspaces, basis and quotient spaces Lecture should be so effective so that the students can grasp the topic easily Lecture Seminar Discussion Assignments Seminar Class Tests 12 2 Two ·   Homomorphism and isomorphism of vector spaces ·   Linear transformations and linear form ·   Dual spaces, Bidual 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 To study Homomorphism of vector spaces and Algebra of Linear transformation Lecture should be so effective so that the students can grasp the topic easily Lecture Seminar Discussion Assignments Seminar Class Tests 22 3 Three ·   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 To study inner Product Spaces Lecture should be so effective so that the students can grasp the topic easily Lecture Seminar Discussion Assignments Seminar Class Tests 10