Subject Code: MA5L001 Subject Name: Linear Algebra L-T-P: 3-0-0 Credit: 3
Pre-requisite(s): Nil
Vector spaces over fields, subspaces, bases and dimension; Systems of linear equations, matrices, rank, Gaussian elimination; Linear transformations, representation of linear transformations by matrices, rank-nullity theorem, duality and transpose; Determinants, Laplace expansions, cofactors, adjoint, Cramer's Rule; Eigenvalues and eigenvectors, characteristic polynomials, minimal polynomials, Cayley-Hamilton Theorem, triangulation, diagonalization, rational canonical form, Jordan canonical form; Inner product spaces, Gram-Schmidt orthonormalization, orthogonal projections, linear functionals and adjoints, Hermitian, self-adjoint, unitary and normal operators, Spectral Theorem for normal operators; Rayleigh quotient, Min-Max Principle. Bilinear forms, symmetric and skew-symmetric bilinear forms, real quadratic forms, Sylvester's law of inertia, positive definiteness.
Text Books:
  1. Axler S. Linear Algebra Done Right, UTM, Springer
  2. Artin M. Algebra, Prentice Hall of India
Reference Books:
  1. Hoffman K. and  Kunze R. Linear Algebra, Pearson Education
  2. Lang S. Linear Algebra, Undergraduate Texts in Mathematics, Springer-Verlag, NewYork
  3. Rose  H.E.  Linear Algebra, Birkhauser
  4. Strang G. Linear Algebra and its applications, Cengage Learning