LINEAR ALGEBRA
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 S0(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. Recommended Books
- 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 edition, Prentice-Hall of India, 1992