- Docente: Mirella Manaresi
- Credits: 9
- SSD: MAT/03
- Language: Italian
- Moduli: Mirella Manaresi (Modulo 1) Monica Idà (Modulo 2)
- Teaching Mode: Traditional lectures (Modulo 1) Traditional lectures (Modulo 2)
- Campus: Bologna
- Corso: First cycle degree programme (L) in Mathematics (cod. 8010)
Learning outcomes
At the end of the course the students know some fondamental concepts of linear algebra (matrices, linear systems, vector spaces, linear maps) and can apply them to the solution of problems from analytic geometry.
Course contents
Matrix calculus, determinants. Systems of linear equations
and matrix calculus: Gauss methods for their solutions.
Vector calculus and cartesian geometry: dot product, cross product.
Geometry of plane and space, lines, planes and their relative
position. Basic Linear Algebra: Vector spaces, subspaces.
Notions of linear dependence and independence. Basis and systems of
generators for a vector space. Existence of basis. Dimension of a
vector space and of its subspaces. Grassmann relation, direct sum
of vector spaces. Linear maps. Kernel and image of a linear map.
The vector space of linear maps. Dual of a vector space. Linear maps and matrices. The matrix associated with a
linear map. Canonical forms for endomorphisms: Endomorphisms of a
vector space, eigenvalues and eigenvectors. Diagonalizability:
necessary and sufficient conditions.
Readings/Bibliography
There is no official textbook. The following books, and many
others, may be useful:
M.Abate: Geometria (McGraw Hill)
S.Greco - P.Valabrega
: Lezioni di
Geometria. Volume I: algebra lineare. Volume II: geometria
analitica. Ed.
Levrotto e Bella, Torino
E.Sernesi: Geometria 1 (Bollati Boringhieri)
Teaching methods
Lectures at the blackboard and discussion of exercises, office
hours.
Assessment methods
The exam consists of a written and an oral examination. The written
part will check the ability of the student to solve problems
concerning the linear geometry of three-dimensional space,
the solution of systems of linear equations, the study of linear
maps and diagonalization of endomorphisms of vector spaces.
The oral part will verify that the basi concepts and theorems
have been understood in a satisfactory way allowing the student to
effectively apply them.
Teaching tools
Lectures with exercise sessions. Sheets of exercises will be handed
out during the lectures (see http://www.dm.unibo.it/~manaresi/
and http://www.dm.unibo.it/~ida/
) , in addition to the ones available in the suggested
textbooks.
In the office hours students will be coached individually.
Links to further information
http://www.dm.unibo.it/~manaresi/
Office hours
See the website of Mirella Manaresi
See the website of Monica Idà