MAA206 - Euclidean and Hermitian Spaces (2022-2023)

Euclidean and Hermitian Spaces continues
the study of linear maps between
vector spaces, started in MAA101. The
goal is to obtain simple and efficient
models for these applications up to suitable
changes of coordinates. The concept
of duality is initially introduced in the
general context of mere vector spaces.
Then, the focus is put on vector spaces
enjoying a richer structure, namely
prehilbert spaces, which is available in
most applications (e.g. in solid mechanics
or in quantum mechanics). The geometry
of these spaces, as well as their important
transformations (e.g. normal or unitary
maps) is also discussed.



Algebra (MAA 206) is a continuation of Algebra (MAA 201) and covers objects in bilinear algebra. These objects, mainly quadratic forms, have fundamental applications (e.g. in Number Theory and Mechanics), and also lead to the study of algebraic objects; for instance, some special groups of matrices, whose applications in mathematics and physics are fundamental, from Number Theory and geometry to the classification of particles.