- Docente: Nicoletta Cantarini
- Credits: 9
- Language: Italian
- Moduli: Nicoletta Cantarini (Modulo 1) Francesco Meazzini (Modulo 2)
- Teaching Mode: Traditional lectures (Modulo 1) Traditional lectures (Modulo 2)
- Campus: Bologna
- Corso: First cycle degree programme (L) in Mathematics (cod. 8010)
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from Sep 18, 2023 to Dec 22, 2023
Learning outcomes
The aim of the course is to introduce the basic fundamental concepts in linear algebra (vector spaces, linear maps) and to relate them with the basic theory of fields.
Course contents
- Rings and fields
- Vector spaces (over a field)
- Subspaces, bases, dimension. Grassmann's formula
- Linear applications
- Matrices associated with a linear application
- Rank theorem and its consequences
- Linear systems
- Change of the basis
- Eigenvalues and eigenvectors
- The characteristic polynomial
- Conjugated matrices and invariants
- The problem of the diagonalizability of an endomorphism
- Hom (V, W), the dual space
- The quotient space
- The problem of the triangulation of an endomorphism
Readings/Bibliography
Marco Manetti. Algebra Lineare per Matematici.
https://www1.mat.uniroma1.it/people/manetti/dispense/algebralineare.pdf
S. Lang Algebra Lineare Ed. Bollati Boringhieri
Teaching methods
During the lectures theoretical elements and exercises are continuously alternated. Some problems are suggested to students and then corrected in subsequent lessons. The interventions of the students are stimulated and their questions are solicited. There are specific hours dedicated to free discussion.
Assessment methods
The exam consists of a written test and an oral test. The written test gives access to the oral test and contains a preliminary part in which the student is subjected to three basic level statements. The student must establish, briefly justifying the answer, whether each of these statements is true or false. The correctness of this preliminary part gives access to the correction of the written test.
Teaching tools
Lessons are taught on the blackboard. It is considered essential that the student can have an eye on the whole reasoning and its consequences during the lesson.
Links to further information
http://www.dm.unibo.it/~nicoletta.cantarini/didattica/Geo1/Geometria1A.html
Office hours
See the website of Nicoletta Cantarini
See the website of Francesco Meazzini
SDGs
This teaching activity contributes to the achievement of the Sustainable Development Goals of the UN 2030 Agenda.