Descriptif

Prerequisites: MAA104, MAA105
MAA201 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.