Linear Algebra - II (MATH206)
Vector spaces, subspaces, basis and dimension, coordinates, row equivalence. Linear transformations, representation by matrices, linear functionals, dual. Algebras, algebra and factorization of polynomials. Commutative rings, determinant function, permutations and properties of determinants. Characteristic values, the Cayley-Hamilton theorem, invariant subspaces, direct-sum decompositions, the primary decomposition theorem, cyclic decompositions and rational form, the jordan form, inner product spaces.