Vector spaces: Basis and dimension, Direct sums.
Determinants: Theory of determinants, Cramer’s rule.
Linear transformations: Rank-nullity theorem, Algebra of linear
transformations, Dual spaces. Linear operators, Eigenvalues and eigenvectors,
Characteristic polynomial, Cayley- Hamilton theorem, Minimal polynomial,
Algebraic and geometric multiplicities, Diagonalization, 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.
Linear groups: Classical linear groups, SU2 and SL 2(R).
Artin, M., Algebra, Prentice-Hall of India, 1994.
Herstein, I. N., Topics in Algebra, Vikas Publications, 1972.
Strang, G., Linear Algebra and its Applications, Third Edition, Saunders,