The course aims to supply students with concepts and computational algorithms that enable them to deal with topics that can be modeled by using linear algebra or affine geometry.
D1 - Knowledge and understanding:
By the end of the course the student is supposed to know the basic concepts of linear algebra, and to understand the meaning of the main theorems related to such concepts.
D2 - Capability to apply knowledge and understanding:
The student will be able to apply effectively the computational algorithms he learned in the course.
D3 - Making judgements:
The student will be able to evaluate whether for a given situation it is possible to produce a model by using linear algebra or affine geometry.
D4 - Communication skills:
The student will be able to understand, describe, explain situations where concepts and methods of linear algebra and/or affine geometry are used.
D5 - Learning skills:
The student will be able to follow explanations, or arguments, given in other courses of his/her curriculum, that use concepts and methods he/she learned in the course.

A working knowledge of the real numbers, their operations and the main properties of these operations. Manipulation of polynomials in one variable.

Systems of linear equations. Vector spaces. Affine geometry of the plane and the space. Matrices. Determinants.
Linear maps. Diagonalization. Brief outline of Euclidean vector spaces.

Main text:
Francesco Bottacin: Algebra Lineare e Geometria, Società Editrice Esculapio

Auxiliary texts:
Edoardo Sernesi: Geometria 1, Bollati Boringhieri

Matrices. Product of matrices and their main properties. Inverible matrices. Systems of linear equations. Existence of solutions. Rouche'- Capelli's Theorem. Gauss elimination algorithm. Elementary operations on the rows (or columns) of a matrix. Vector spaces, subspaces. Linearly independent vectors. Generating set for a vector space. Bases, dimension. Rank of a matrix. Determinants. Binet's Theorem. Linear maps, their kernel and image. Dimension theorem for a linear map. Matrices associated to a linear map. Eigenvalues and eigenvectors for an endomorphism. Diagonalization. (Brief outline) Scalar products on real spaces, their main properties. Triangular and Cauchy-Schwarz inequalities. Angles, orthogonal directions. Orthogonal subspace associated to a given subspace of an euclidean vector space.

Frontal lectures on the theory. Exercises classes at the blackboard and with technological support.

Any change to the methods here described, which would become necessary to ensure the application of the safety protocols related to the COVID19 emergency, will be communicated on the Department website, Study Course website and Course website.

For texts of past written examinations, their correction and for other teaching material, see the website of the course at
http://moodle2.units.it/

The exam program coincides with the arguments of the lectures. The written test consists in answering to a theoretical question, including two definitions and a theorem with proof (7 points), and in solving three exercises modeled on those solved during the lectures (8/9 points each). During the written test, one may not consult neither books nor notes, but only an A4 sheet of paper with handwritten notes on a single side, kept well visible during the test. To be admitted to the oral test it is necessary to pass the written test with a score not less than 15/30. In this case, the oral test can be given in any session of the same academic year. Handing in a written test substitutes any previous written test if the new grade is higher than the current one; if the new grade if lower than or equal to the previous one, the grade of the written part is the average (rounded up) of the new grade with the current one. The oral test consists in verifying the comprehension of the contents (definitions, statements, and proofs) and the ability in explaining the subject. The final grade depends on both written and oral. To obtain a passing grade (18/30), a student should know the very basic definitions and results presented in the course. The grade increases according to the extent and the depth of the knowledge of the student, in terms of technical details and also of quality, clarity and precision of the presentation. To obtain the highest grade, a student should show very good command of the topic, denoted for example by the ability to address questions related to the course, but not explicitly taught in the lectures. To ensure the access to aids at the exam from students with disabilities, specific learning disorder (SLD), or special educational needs (SED), please preemptively contact the University's Disability Service or SLD Service.