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• Week 01: Introduction to vector spaces, examples and preliminary results
• Week 02: Linear combination of a set of vectors, Linear span of a set of vector space, properties and related results.
• Week 03: Linearly dependent set of vectors and Linearly independent set of vectors: Definition, examples and results
• Week 04: Subspace: Definition, examples and related results.
• Week 05: Basis of a vector space: Definition, examples and related results
• Week 06: Dimension of a vector space: Definition, examples and related results
• Week 07: Cosets, Quotient Spaces, dimension of quotient space, dimension of sum of subspaces
• Week 08: Coordinates and change of basis, Linear transformation: Definition, examples and related results
• Week 09: Mid Term Examination
• Week 10: Space of linear transformations and its dimension
• Week 11: Rank and Nullity of linear transformation, matrix of linear transformation
• Week 12: Inner Product Spaces
• Week 13: Dual Space and Annihilator of subspace
• Week 14: Orthonormal basis and orthogonal complements
• Week 15: Gramm-Schmidt process of orthogonalizations
• Week 16: Eigen values and eigen vectors
• Week 17: Similar matrices and diagonalization
• Week 18: Final Term Exams