The space R^n of n-tuples of real numbers. Matrices and their algebraic properties. Linear systems, Gauss algorithm. Standard scalar product and norm in R^n. Complex numbers. Vector spaces, subspaces; linearly independent vectors, generators, bases, dimension. Rank of matrices. Linear maps, kernel, image. Determinant. Eigenvalues and eigenvectors. Diagonalization.
Notes provided by the Teacher.
Abate, Algebra Lineare
Nicholson, Algebra Lineare
Robbiano, Algebra Lineare
The course aims to provide the students with fundamental knowledge and understanding in Linear Algebra starting from the language of matrices, which is important for the subsequent career.. One of the aims is to let the students develop basic technical skills, and critical thinking, needed when modelling and solving mathematical problems in different settings. Special attention will be paid to help the students to develop communication skills necessary for teamwork. The course covers topics and provides learning skills that are needed, or strongly suggested, to pursue a degree in Computer Sciences or in any scientific subject.
Courses to be used as requirements (required and / or recommended)
Courses required: None
Recommended Courses: None
Lectures: Presentation of the theory described in the course program, with teacher-student direct interaction, to ensure a full understanding of the subject.
Students will also be guided to modelling and solving a wide selection of problems in Linear Algebra. The training sessions are conducted so to:
-- help the students develop communication skills and apply the theoretical knowledge;
-- encourage independent judgement in the students.
Moodle learning platform: online teacher-student interaction, posting of additional notes, weekly exercise sheets, examples of tests.
The suggested reading includes supplementary material that may be useful for further personal studies in mathematics or in any scientific subject.
Type of Assessment
Assements Method: Written Test.
Alternatively it is possible to take advantage of the intermediate tests during the term.
In the tests it is proposed a selection of exercises and a number of questions. Exercises are designed to assess the ability of the students to apply their skills to problem modelling and solving. In the evaluation, special attention is paid to the correctness of the solution procedure, as well as to the originality and effectiveness of the methods adopted. The questions are designed to evaluate the degree of understanding of the theory presented in the course. In the assessment, special attention is paid to communication skills, critical thinking and appropriate use of mathematical language.
The space R^n of n-tuples of real numbers. Matrices and their algebraic properties. linear systems, Gauss algorithm. Standard scalar product and norm in R^n. Complex numbers. Vector spaces, subspaces; linearly independent vectors, generators, bases, dimension, coordinates. Space generated by the columns of a matrix, generated by the row space. Rank. Linear maps, kernel, image. Rouche-Capelli and the structure of solutions of a linear system. Linear applications and matrices. Determinant: axiomatic definition of the determinant function, its properties and calculations by elimination of Gauss. Eigenvalues and eigenvectors. Diagonalization, orthogonal diagonalization.