MA 219: Linear Algebra

Credits: 3:1

Prerequisite courses for Undergraduates: UM 102

Vector spaces: Definition, Basis and dimension, Direct sums. Linear transformations: Definition, Rank-nullity theorem, Algebra of linear transformations, Dual spaces, Matrices.

Systems of linear equations: Elementary theory of determinants, Cramer’s rule. Eigenvalues and eigenvectors, the characteristic polynomial, the Cayley- Hamilton Theorem, the minimal polynomial, algebraic and geometric multiplicities, Diagonalization, The Jordan canonical form. Symmetry: Group of motions of the plane, Discrete groups of motion, Finite groups of SO(3). Bilinear forms: Symmetric, skew symmetric and Hermitian forms, Sylvester’s law of inertia, Spectral theorem for the Hermitian and normal operators on finite dimensional vector spaces.  

Suggested books and references:

  1. Artin, M., Algebra, Prentice Hall of India, 1994.
  2. Halmos, P., Finite dimensional vector spaces, Springer-Verlag (UTM), 1987.
  3. Hoffman, K. and Kunze, R., Linear Algebra (2nd Ed.), Prentice-Hall of India, 1992.

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Contact: +91 (80) 2293 2711, +91 (80) 2293 2265 ;     E-mail: chair.math[at]iisc[dot]ac[dot]in
Last updated: 19 Jul 2024