# Course Details for A.Y. 2016/2017

#### Name:

**Geometria A / Geometry A**

### Basic information

##### Credits:

*:* Bachelor Degree in Mathematics 12 CFU (a)

##### Degree(s):

Bachelor Degree in Mathematics 1^{st} anno curriculum Generale Compulsory

##### Language:

Italian

### Course Objectives

The goal of the course is to make the student familiar with the basic and more
advanced linear algebra theory of linear algebra and with analytic geometry in
the plane and in the 3-dimensional space.
The student should also become acquainted with the problem of diagonalization
of a matrix or their Jordan canonical form and also with quadratic forms and
their canonical form.
A particular family of plane curves is presented: the conics and
their affine, metric and projective classification.

### Course Content

- Matrices and systems of linear equations.
- Vector spaces and change of bases.
- Linear transformations and matrices associated to them.
- Eigenvalues, eigenvectors and diagonalization.
- Euclidean spaces. Inner product. Cross product. Orthogonal subspaces.
Gram-Schmidt orthogonalization.
- Affine and euclidean geometry.
- Eigenvalues and eigenvectors of symmetric matrices. Spectral theorem.
- Unitary and Hermitian matrices. Diagonalization of an hermitian matrix. Hermitian product.
- Bilinear forms, quadratic forms and their canonical form.
- Conics and their affine and metric classification.
Projective space. Homogeneous coordinate. Projective classification of conics.
- Isometries of euclidean spaces of dimension two and three.
- Jordan canonical form of a matrix.

### Assessment Methods and Criteria

Written and Oral Exam

### Textbooks

- Nicholson W.K. , Algebra lineare. Dalle applicazioni alla teoria , McGraw-Hill. ulteriore testo utile
* *
- Fania, M.L. , Appunti del corso di Geometria A, a.a. 2015/2016 testo di riferimento
* *
- Apostol T.M., Calcolo, volume secondo Geometria , Boringhieri. ulteriore testo utile
* *
- Campanella G., Esercizi di Algebra Lineare e Geometria , Aracne. ulteriore testo utile
* *
- Sernesi E. , Geometria 1 , Boringhieri . testo di riferimento
* *
- Flamini F., Verra A. , Matrici e Vettori. Corso di base di geometria e algebra lineare , Carocci . ulteriore testo utile
* *

### Notes

- I Fisici mutuano i primi 9 CFU del corso, corrispondenti ai primi otto punti del programma.

### Course page updates

This course page is available (with possible updates) also for the following academic years:

** To read the *** current * information on this course, if it is still available, go to the university course catalogue .
*Course information last updated on: 07 ottobre 2016, 23:02*