Linear Algebra
Vector spaces :Basis and dimension, Direct sums. Determinants :Theory of determinants, Cramerâs 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 SO(3). Bilinear forms :Symmetric, skew symmetric and Hermitian forms, Sylvesterâs 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). Recommended books
- 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, 1988.
- Halmos, P., Finite dimensioinal Vector spaces, Springer-Verlag (UTM), 1987.
- Hoffman, K. and Kunze, R., Linear Algebra, 2nd Edition, Prentice Hall.