AIMS AND LEARNING OUTCOMES

At the end of the course the student will be able to:

- give correct definitions of the objects and properties studied, using the appropriate mathematical formalism;

- recognize in concrete examples the geometrical objects and the algebraic properties studied;

- describe the set of solutions of systems of linear equations;

- solve exercises of plane and space geometry involving points, lines, planes, angles, distances, scalar products, orthogonal projections, conics, quadrics;

- give explicit examples of objects that satisfy the geometrical or algebraic properties studied;

- apply the notions and procedures studied in order to solve problems, also of new types and of an abstract nature.

PREREQUISITES

Basic arithmetic skills in computations and manipulations of algebriac formulas. Trigonometry.

TEACHING METHODS

Frontal lessons in class. Some exercises will be posted on Aulaweb. Attendance is strongly recommended.

SYLLABUS/CONTENT

Complex numbers: algebraic and trigonometric form. Solutions to z^n=a. Fundamental theorem of algebra.

Polynomials: roots and multiple roots. Ruffini’s theorem. Factorization of polynomials in R[X].

Algebraic operations on matrices. Invertibility of matrices.

Gaussian elimination

Determinant and rank of a matrix. Laplace expansion, Cramer theorem, Rouché-Capelli’s theorem.

Vector spaces and linear maps.

Diagonalization of endomorphisms. Eigenvalues and eigenvectors. Characteristic polynomial.

Vector algebra in the plane and the space.

Real symmetric matrices

RECOMMENDED READING/BIBLIOGRAPHY

The following notes will be posted on Aulaweb:
1. Appunti di Geometria e Calcolo numerico (A. Perelli e M.V. Catalisano)
2. Appunti di Algebra Lineare (M.E. Rossi).
3. Appunti di Geometria (G. Niesi)
Recommended book:  Algebra Lineare a Geometria Analitica (F. Odetti, M. Raimondo), ECIG Universitas.