Syllabus: Real vector spaces, subspaces, spanning sets, basis sets, dimension of a vector space. Solution of a system of linear equations. Row space and column space of a matrix, rank of a matrix, elementary row and column operations of a matrix. Inversion of square matrices, rank factorization of a matrix. Properties of determinants. Linear transformations, range and null space of a linear transformation, rank-nullity theorem. Matrix representation of a linear transformation. Inner product spaces, normed linear spaces, examples of different normed linear spaces, orthonormal basis sets. Eigenvalues, eigenvectors, characteristic polynomials. Spectral theorem for real symmetric matrices. Singular value decompositions.
- A. R. Rao and P. Bhimsankaram: Linear algebra, Hindustan book agency, 2000.
- S. H. Friedberg, A. J. Insel and L. E. Spence: Linear algebra, Pearson, 2015.
- D. C Lay: Linear algebra and its applications, Pearson, 2014.