LINEAR ALGEBRA

The course is one of the basic activities of the Bachelor's Degree in Informatics and its aim is to present the basic ideas and computational techniques of linear algebra. It also includes a wide variety of applications. The course also introduces the student to working with abstract concepts. In covering the basic ideas of linear algebra, the abstract ideas are balanced by considerable emphasis on the geometrical and computational aspects of the subject.
The course finally provides the main notions needed in order to develop applications which use linear programming, artificial intelligence and artificial vision.

Knowledge and understanding:
- knowledge and understanding of the fundamental concepts of linear algebra;
- understanding the feasibility and complexity of solving a complex linear system;
- knowledge of different methodologies for the calculus of determinants, image and kernel of a linear transformation, autovalues and autovectors of matrices.

Ability to apply knowledge and understanding:
- to solve complex linear systems;
- ability of linearly computing.

Elementaty notions of mathematics of secondary school.

Fields and complex numbers.
Linear equations and matrices, operations on matrices, special matrices.
Real vector spaces: linear independence, bases and dimension, rank of a matrix.
Inner product, lines and planes.
Linear transformations and matrices. Kernel and rank of a linear transformation.
The matrix of a linear transformation. vector space of matrices and linear transformations. Duality.
Determinant, inverse matrix.
Autovalues and autovectors. Diagonalisation.

Main book:
A. Salibra: Appunti di Algebra Lineare, 2018 (in italian). http://www.dsi.unive.it/~salibra/appunti-algebra-lineare2017.pdf
Other books:
M. Abate, C. de Fabritiis: Geometria analitica con elementi di algebra lineare, Seconda Edizione, McGraw-Hill, 2010.
A. Facchini, Algebra e Matematica Discreta, Zanichelli 2000.
Claretta Carrara, Esercizi di Algebra Lineare, http://www.dsi.unive.it/$\sim$acarraro/Esercizi\_algebra\_lineare\_2.pdf

The exam consists of a written test. The written test lasts three hours and it is composed by four exercises aimed at verifying:
1) the capability to compute the basic geometrical objects of the plane and space;
2) the ability to algebraically compute with matrices and vectors, and solve linear systems;
3) the knowledge of the basic concepts of linear algebra: basis, linear transformation, determinant and orthogonality;
4) the ability to compute autovalues and autovectors of a linear transformation.

During the written test is not allowed the use of books, notes, electronic media.

Lessons with digital blackboard and traditional blackboard.
Written home work and exercises in the classroom are able to gently introduce the student to linear algebra:
The Line and plane equations. Matrix Calculus to solve linear problems. Eigenvalues and eigenvectors.

Italian

written