Geometry 1

A.Y. 2024/2025
7
Max ECTS
64
Overall hours
SSD
MAT/03
Language
Italian
Learning objectives
The course aims to provide students with some knowledge and skills in linear algebra. Starting from the notion of finite dimensional vector space on any field, we arrive at solving the systems of linear equations with the Gauss-Jordan method. Another goal is to study linear and bilinear applications, illustrating the notion of a representative matrix and the related problems of diagonalization. The bilinear applications are used to investigate Euclidean vector spaces (real and complex) and self-adjoint operators, for which the spectral theorem is fully proved.
Expected learning outcomes
At the end of the course, students will have acquired the following skills:
1. they will be able to solve systems of linear equations;
2. they will be able to apply the theory of finite dimensional vector spaces, recognizing vector subspaces and determining their bases;
3. they will be able to study linear applications, determining the representative matrix, the kernel and the image;
4. they will be able to apply some aspects of the theory of diagonalization of endomorphisms and matrices, based on the search for eigenvalues and eigenvectors;
5. they will know how to work in spaces with a positive definite inner product (also called Euclidean spaces) and apply elementary notions of Euclidean geometry;
6. they will know how to recognize self-adjoint operators and will be able to diagonalize them, determining an orthonormal basis of eigenvectors by means of the spectral theorem (real and complex).
Single course

This course can be attended as a single course.

Course syllabus and organization
Professor(s)
Reception:
by appointment (by e-mail)
Math. Dept. - via C. Saldini 50 - Milano
We use a selection of our own and third-party cookies on the pages of this website: Essential cookies, which are required in order to use the website; functional cookies, which provide better easy of use when using the website; performance cookies, which we use to generate aggregated data on website use and statistics; and marketing cookies, which are used to display relevant content and advertising. If you choose "ACCEPT ALL", you consent to the use of all cookies. You can accept and reject individual cookie types and revoke your consent for the future at any time at "Settings".