Course Plan MTH113M

There will be around 19 Lectures for Linear Algebra. Each lectures will be of 50 minutes. There will be tutorial each week and will be taken by an assigned tutor. Office hours will be provided by tutors. Students can clear their doubts during the office hours or mailing to the respective tutors. Lecture notes are available in the website 

https://sites.google.com/site/abhijitwebpage/lecture-notes-mth113m.

 Feedback and suggestions are always welcome and can be communicated by mailing to abhipal@iitk.ac.in

Linear Algebra: Matrices, System of linear equations, Gauss elimination method, Elementary matrices, Invertible matrices, Gauss-Jordon method for finding inverse of a matrix, Determinants, Basic properties of determinants. Cofactor expansion, Determinant method for finding inverse of a matrix, Cramer's Rule, Vector space, Subspace, Examples, Linear span, Linear independence and dependence, Basis, Dimension, Extension of a basis of a subspace, Intersection and sum of two subspace, Examples. Quotient Space

Linear transformation, Kernel and Range of a linear map, Rank-Nullity Theorem. Rank of a matrix, Row and column spaces, Solvability of system of linear equations, some applications Inner product on Cauchy-Schwartz inequality, Orthogonal basis, Gram-Schmidt orthogonalization process. Orthogonal projection, Orthogonal complement, Projection theorem, Fundamental subspaces and their relations, Applications (Least square solutions and least square fittings). Eigen-values, Eigen-Vectors, Characterization of a diagonalizable matrix. Diagonalization: Example, An application. Diagonalization of a real symmetric matrix. Representation of real linear maps by matrices (optional)