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).  


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Last updated: 21 Jun 2024