Portale di Ateneo - En.Unibs.it

Linear Algebra
Basic notions on sets, relations and functions. Algebraic structures: Groups and fields.
Vector spaces over a field: subspaces, intersections and sums; basis, dimensions and Grassmann formula. Linear forms and transformations between vector spaces. Matrices: determinant and rank, Laplace and Binet theorems. Linear systems: Rouché-Capelli and Cramer theorems, solvability and solution sets. Eigenvalues, eigenvectors and decomposition of an endomorphism.
Bilinear forms, scalar products and Euclidean vector spaces.
Affine and Euclidean spaces
Affine space: definition, translation group, affine subspaces, parallelism. Coordinate system and analytic geometry.
Euclidean space: distances, orthogonality, circles, spheres, basic geometrical loci.
Projective spaces
Projective completion of an affine geometry: projective subspaces, homogenous coordinates and representation of subspaces. Complexification.
Real algebraic curves and surfaces
Order of a plane curve, simple and singular points. Conics: projective classification, pencils of conics, polarity, affine and metric classifications, canonical forms.
Generality on quadrics and their canonical forms.