Linear Algebra (Algebra lineare)
Teacher
Credits
6 CFU
Specific educational objectives
The course aims to provide basic training in the subject Linear Algebra, by treating the concepts of vector space, linear map, matrix, determinant, linear system, eigenvalues and eigenvectors, diagonalizable matrices, real symmetric and Hermitian matrices, squareness, canonization of quadratic forms, classification of conics.
Acquired skills
– Learning and understanding of the basic concepts of linear algebra.
– Basic knowledge of Algebra: Binary Relations, Equivalencies, Groups, Rings, Fields.
– Basic knowledge of Linear Algebra: Vector Spaces, Bases, Homomorphisms, Matrices, Determinants, Linear Systems, Eigenvalues and Eigenvectors, Bilinear forms, Quadratic Forms.
– Basic knowledge of geometry Affine and Euclidean: Plans, Lines, Conic, Quadrics.
Contents
Set theory, functions, relations, equivalence relations. (4 hours)
Algebraic structures: groups, rings, modules, fields. (4 hours)
Vector spaces, bases, dimension, coordinates of a vector. (12 hours)
Linear maps, matrices, rank, determinant, linear systems. (12 hours)
Eigenvectors, eigenvalues and diagonalization. (6 hours)
Bilinear forms, scalar products, symmetric operators. (8 hours)
Applications to geometry: lines, planes, conics and quadrics. (14 hours)
References
– Enrico Schlesinger, Algebra lineare e geometria, Zanichelli.
– Freni Domenico, Jung Kyu Canci, Algebra lineare e geometria, esercizi e complementi, Pearson Italia.
– Exercises and course notes posted on the web by the teacher.
Type of exam
Written and oral.