- Docente: Stefano Riolo
- Credits: 10
- SSD: MAT/03
- Language: Italian
- Teaching Mode: Traditional lectures
- Campus: Bologna
- Corso: First cycle degree programme (L) in Astronomy (cod. 8004)
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from Sep 24, 2024 to Dec 19, 2024
Learning outcomes
Once the course is concluded, the student gets the fundamental notions on vector spaces and linear mappings, and is able to solve simple problems of analytic geometry.
Course contents
Preliminaries: sets and functions, number sets, modular arithmetic, polynomials, complex numbers, groups and fields.
Linear systems: resolution, relation with vector spaces and affine spaces, applications to affine geometry.
Matrices: matrix multiplication, invertibility, similarity, congruence, determinant, canonical Jordan form.
Vector spaces: subspaces, generators, linear independence, bases, coordinates, dimension, Grassmann formula, change of basis.
Linear maps: kernel and image, rank theorem, associated matrices, endomorphisms (determinant, eigenvalues and eigenvectors, digonalisability, nilpotence), dual vector space.
Bilinear and quadratic forms: associated matrices, diagonalisability, rank and signature, Sylvester theorem, positive definite scalar products and norms (Cauchy-Schwartz inequality, orthogonality, angles, isometries, Euclidean spaces), Hermitian products, spectral theorem.
Readings/Bibliography
Main book: B. Martelli - https://people.dm.unipi.it/martelli/alg_lin.html (pdf)
Exercises: S. Francaviglia - "Geometria e Algebra T"Teaching methods
Traditional lessons, individual and collective meetings. Weekly exercise sessions and tutoring.
Assessment methods
The exam consists of a written test and an oral examination. The written test may be carried out in the traditional way at the end of the course, or by means of some partial tests during the course.
Teaching tools
Links to further information
https://www.unibo.it/sitoweb/stefano.riolo/avvisi
Office hours
See the website of Stefano Riolo