Week - 1:Introduction to binary operations, Vector spaces, subspaces.
Week - 2:Linearly independent and dependent vectors..
Week - 3:Basis of vector spaces, Linear functions, Row equivalent matrices.
Week - 4:Null spaces, Four subspaces associated with the matrix, Diagonal dominant matrices.
Week - 5:Coordinate of a vector, Linear transformation.
Week - 6:Range space and Null space of Linear transformation, Rank-Nullity theorem.
Week - 7:Matrix representation of Linear transformation, Similar matrices, Orthonormal bases.
Week - 8:Gram-Schmidt orthogonalisation process, QR factorisation, Inner product spaces.
Week - 9:Vector norm, Matrix norm, Sensitivity analysis.
Week - 10:Orthogonal matrix, Least square method, Jordan-Canonical form.
Week - 11:Singular value decomposition (SVD).
Week - 12:Moore-Penrose inverse, Householder transformation.