- Docente: Rita Fioresi
- Credits: 10
- SSD: MAT/03
- Language: Italian
- Moduli: Rita Fioresi (Modulo 1) Emanuele Latini (Modulo 2)
- Teaching Mode: Traditional lectures (Modulo 1) Traditional lectures (Modulo 2)
- Campus: Bologna
- Corso: First cycle degree programme (L) in Physics (cod. 9244)
Learning outcomes
At the end of the course, the student knows the theory of vector spaces (real and complex) of finite dimension and linear applications. He also acquires the fundamental notions of analytic geometry in the plane and in space. In particular, the student is able to: solve linear systems; search for eigenvectors and eigenvalues; diagonalizing real symmetric matrices and Hermitian matrices; solve simple geometry problems.
Course contents
Three-dimensional geometry of space. Vector spaces, dimension bases. Linear maps, dimension theorem. Linear systems, Rouche'-Capelli theorem. Scalar products, spectral theorem. Dual space, notes on tensors.
Readings/Bibliography
Linear Algebra, S. Lang
Teaching methods
Lectures
Assessment methods
Written and oral exam
Written exam: it consists of 6 exercises each rated at a maximum of 5 points for a total of 30 points. The exercises cover the whole course program starting from Euclidean geometry, linear, determinant and inverse applications, eigenvalues and eigenvectors, up to dealing with applications of the spectral theorem and the concepts of dual space and tensors. The student will be admitted to the oral if he achieves a score of at least 18/30. Oral exam: consists of a discussion of the written test with in-depth analysis of the questions that have not been given an exhaustive treatment. The final mark is the average of the written and oral marks.
Teaching tools
See website Fioresi
Office hours
See the website of Rita Fioresi
See the website of Emanuele Latini