The course provides an introduction to linear algebra and analytic geometry, with particular focus on matrix computations, on vector spaces and on solving linear systems and analitical geometry problems in 2 and 3 dimensions.
The teaching aims to provide basic knowledge of linear algebra and analytical geometry, with particular attention to matrix calculus, vector spaces, the resolution of linear systems and analytical geometry problems in space.
Computation of expressions with complex numbers. Roots of a complex number. Roots and factorization of polynomials. Calculations with matrices and linear maps. Solving systems of linear equations. Vector operations. Solving geometric problems by means of vectors, matrices, cartesian coordinates, and algebraic equations. Identification and canonical form of conics.
Elementary knowledge of arithmetic, algebra, trigonometry, set theory.
The course consists of 52 hours of lectures and practices. In the lectures the topics of the syllabus are explained with definitions, theorems and some proofs, which can be useful for the comprehension of the topics and to develop the logical and deductive skills. Every theoretical topic is explained with examples and exercises.
Sets and maps. Complex numbers and polynomials. Linear systems and gaussian elimination. Matrices, determinants, rank. Vector spaces. Vectors in geometry. Subspaces, bases, dimension. Linear maps. Matrices related to a linear map. Eigenvalues, eigenvectors. The diagonal form of a matrix. Quadratic forms. Systems of cartesian coordinates, linear changes of coordinates. Points, lines and planes: cartesian and parametric equations, parallelism, angles, distances, orthogonal projections. Conics.
Web Resources: http://www.diptem.unige.it/catalisano/default.htm
Ricevimento: By appointment, via e-mail: mariavirginia.catalisano@unige.it
MARIA VIRGINIA CATALISANO (President)
VALENTINA BERTELLA
SERGIO DE MICHELI
September 15, 2025
The timetable for this course is available here: EasyAcademy
The examination consists of a written part and an oral discussion. The written part is made up of 10 questions that cover all the material of the course.
The use of notes, books, or electronic devices is forbidden.
The questions of the written part will verify both the operational skills through problem solving and the learning of the theory, such as definitions and theorems. During the oral test there will be a discussion about the written part and two to three additional questions.
