italian version

Aims :

Produce basic information and skills of Linear Geometry (Vector Spaces,
Linear mappings, Matrix Calculus, Linear Systems, Affine and Euclidean Geometry, Eigenvalues and Eigenvectors.

Topics :

Abstract Vector Spaces, R^n e C^n
Vector subspaces. Linear independence and Dependance.
Bases. Standard Basis. Dimension.
Affine Spaaces. Lineas and Planes: parametric and cartesion equations.
Linear Mappings. Matrix associated to Linear Mappings.
Matricial Calculus. Determinants. Inverse Matrix.
Linear Systems. Rouché-Capelli and Cramer Theorems. Row Reduced Echelon Form.
Euclidean Spaces. Scalar products. Ortogonalità. Distances. Pytagora Theorem.
Gram-Scmidt Orthogonalization. Orthogonal Projection. Symmetries.
Self-values and Self-vectors. Characteristic Polinomial.

Textbooks :

-1) Marco Abate: Algebra Lineare. McGraw-Hill, Aprile 2000 o successive edizioni.
-2) Marco Abate e Chiara De Fabritiis: Esercizi di Geometria, McGraw-Hill

Exam :

Written and oral.

Tutorial Session :

Available after the 2005/06 Class Schedule.