- Docente: Stefano Riolo
- Credits: 10
- SSD: MAT/03
- Language: Italian
- Moduli: Stefano Riolo (Modulo 1) Enrico Fatighenti (Modulo 2)
- Teaching Mode: Traditional lectures (Modulo 1) Traditional lectures (Modulo 2)
- Campus: Bologna
- Corso: First cycle degree programme (L) in Astronomy (cod. 8004)
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from Sep 26, 2023 to Dec 19, 2023
Learning outcomes
Once concluded the course, 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.
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.
Linear systems: resolution, relation with vector spaces and affine spaces, applications to affine geometry.
Matrices: matrix multiplication, invertibility, similarity, congruence, determinant, canonical Jordan form.
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.
Readings/Bibliography
Main book: B. Martelli - "Geometria e Algebra Lineare" (pdf)
Extra notes: K. G. O'Grady - "Algebra Lineare e Geometria" (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
See the website of Enrico Fatighenti