Algebra II E 1100-1Ind06

In the course we will continue to present important concepts of linear algebra. With some background material introduced in the course "Algebra I" we will focus more on analysis of linear operators, functional calculus and elements of analytic geometry. Towards the end of the semester we will deal with basics of abstract algebra.

Program:
1. Multilinear algebra and determinants - continued
(quadratic forms, diagonalization, bilinear forms on real vector spaces, signature, positivity, symplectic spaces)
2. Spectrum of an operator
(spectrum of an operator, eigenvectors, diagonalizable operators, Jordan basis, Jordana form)
3. Functional calculus
(the space of linear maps, functions of an operator)
4. Unitary spaces
(scalar products, unitary spaces, orthogonal projections, self adjoint and unitary maps, the spectral theorem in finite dimensional spaces)
5. Additional topics
(groups - permutations, roots of unity, linear groups, rings, algebras, modules, representations, affine spaces, affine maps)