Course Details

1 Title of the course
(L-T-P-C)
Linear Algebra (1st Half)
(3-1-0-4)
2 Pre-requisite courses(s)
3 Course content Vectors in Rn, notion of linear independence and dependence, linear span of a set of vectors, vector subspaces of Rn, basis of a vector subspace. Systems of linear equations, matrices and Gauss elimination, row space, null space, and column space, rank of a matrix. Determinants and rank of a matrix in terms of determinants. Abstract vector spaces, linear transformations, matrix of a linear transformation, change of basis and similarity, rank-nullity theorem. Inner product spaces, Gram-Schmidt process, orthonormal bases, projections and least squares approximation. Eigenvalues and eigenvectors, characteristic polynomials, eigenvalues of special matrices (orthogonal, unitary, hermitian, symmetric, skew-symmetric, normal). Algebraic and geometric multiplicity, diagonalization by similarity transformations, spectral theorem for real symmetric matrices, application to quadratic forms.
4 Texts/References
  1. H. Anton, Elementary linear algebra with applications (8th Edition), John Wiley (1995).
  2. G. Strang, Linear algebra and its applications (4th Edition), Thomson (2006)
  3. S. Kumaresan, Linear algebra - A Geometric approach, Prentice Hall of India (2000)
  4. E. Kreyszig, Advanced engineering mathematics (10th Edition), John Wiley (1999)