Programme

Systems of linear equations. Coefficient matrix. Matrix addition and scalar multiplication. Gauss-Jordan elimination. Row by Column multiplication. Determinant. Invertible matrices. Rank of a matrix and Rouche'-Capelli Theorem. Geometric vectors. Vector spaces and subspaces. Generators and linearly independent vectors. Basis and dimension. Linear maps. Kernel and image of a linear map. Rank plus nullity Theorem. Matrix associated with a linear map. Diagonalization of linear maps.

Core Documentation

F. Flamini; A. Verra: “Matrici e vettori -Corso di base di geometria e algebra lineare” Carocci ed.

Reference Bibliography

W. Keith Nicholson: “Linear algebra with applications”. McGraw-Hil.

Type of delivery of the course

Frontal lessons and exercises

Type of evaluation

Written exam

Programme

Linear Algebra:
Matrices. Determinants. Rank. Linear systems. Vector spaces. Linear applications. Eigenvalues ​​and eigenvectors.
Diagonalization. Scalar product. Symmetric operators. Spectral theorem.
Geometry:
Affine geometry of the plane and space. Euclidean geometry of the plane and space.

Core Documentation

F. Flamini, A. Verra: Matrici e vettori. Corso di base di geometria e algebra lineare. Carocci.
Also suggested:
E. Schlesinger: Algebra lineare e geometria, Zanichelli.
L. Mauri e E. Schlesinger: Esercizi di algebra lineare e geometria, Zanichelli.

Type of delivery of the course

Lessons in presence, 4 hours per week, according to the academic calendar. Self-assessment exercises will be assigned to be carried out at home. It is suggested tostudy and practice the topics as they are presented.

Type of evaluation

written examination, with calculation questions but also theoretical ones (possible oral colloquium).