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