# ALGEBRA LINEARE E GEOMETRIA A - L

Academic Year 2020/2021 - 1° Year - Curriculum Elaborazione Dati e Applicazioni and Curriculum Sistemi e Applicazioni
Teaching Staff: Paola BONACINI
Credit Value: 6
Scientific field: MAT/03 - Geometry
Taught classes: 24 hours
Exercise: 24 hours
Term / Semester:

## Learning Objectives

• Knowledge and understanding: The aim of the course is to give the basics of linear algebra and analytic geometry that are useful to interpret and describe problems in computer science.
• Applying knowledge and understanding: the student will acquire the skills necessary to deal with typical issues of discrete mathematics, solving classical problems where standard techniques are required.
• Making judgements: the student will be able to independently develop solutions to the main problems of the course by choosing the most convenient strategy based on the learning outcomes.
• Communication skills: the student will acquire the necessary communication skills by acquiring the speciﬁc language of linear algebra and geometry.
• Learning skills: The aim of the course is to provide the study method to the students, the forma mentis and the logical rigor that will be needed in order to solve autonomously new problems that may arise during a work activity.

## Course Structure

Should teaching be carried out in mixed mode or remotely, it may be necessary to introduce changes with respect to previous statements, in line with the programme planned and outlined in the syllabus.

.Learning assessment may also be carried out on line, should the conditions require it.

## Detailed Course Content

1. Calculation of matrix algebra and linear systems. Matrices. Matrix operations. Linear systems *. Calculating the inverse matrix. Determinant of a square matrix and its properties. Rank of a matrix. Cramer's theorem and Rouche-Capelli.
2. Vector spaces. Subspaces and transactions between them. Subspace sum. Linear independence and linear dependence. Bases and dimension of a vector space. Eigenvalues and eigenvectors. Characteristic polynomial. Research of the eigenvalues and eigenspaces associated with them. Similarity between matrices. Diagonalizable matrices.

1. Vector Calculus. Applied vectors. Decomposition theorem. Scalar product and cross product. Mixed product. Free vectors.
2. Linear geometry in the plane. Lines in the plane and their equations. Parallelism and squareness. Intersection between plane and lines. Homogeneous coordinates in the plane. Bundles of straight.
3. Isometries. Translation, rotation around a point. Reﬂection.
4. Linear geometry in space. Planes and lines in space and their equations. Parallelism and squareness. Intersection between planes, between a plane and a straight line and between lines. homogeneous coordinates in space. Improper points and lines in space. Bundles of plans.
5. Conics and their associated matrices. Orthogonal Invariants. Irreducible and degenerate conics. Discriminant of a conic. Canonical reduction of a conic. Parabolas, Ellipses, Hyperbolas equations, center and axis. Circumferences, Tangents of conics.

## Textbook Information

1. Appunti in rete alla pagina web https://andreascapellato.wordpress.com/didattica-2/
2. S. Giuffrida, A. Ragusa, Corso di Algebra Lineare, Il Cigno Galileo Galilei Roma.
3. G. Paxia, Lezioni di Geometria, Cooperativa Universitaria Libraria Catanese.
4. S. Greco, B. Matarazzo, S. Milici, Matematica Generale, G. Giapichelli Editore, 2016.