italian version

Aims :

Students must be able to use the tools of analytic geometry and linear algebra and to apply them to the solving of scientific and technological problems.

Topics :

Vector spaces. Basis of a vector space, coordinates. Dimension of a vector space. Grassman’s theorem. Linear maps. Kernel and image of a linear map. Dimension theorem. Linear systems. Rouche’s theorem. Ladder reduction. Operation on matrices and linear maps. Sum and composition of linear maps. Isomorphisms. Product of matrices. Invertible matrices. Change of basis.. Matrix associated to a linear map with respsct to two basis. Similar matrices. Determinant. Affine geometry. Equations of lines and planes. Mutual position of points, lines and planes; incidence and parallelism conditions. Change of affine coordinate system. Eigenvalues and eigenvectors. Triangolable and diagonalizable endomorphisms. Characteristic polynomial. Algebraic and geometric multiplicity. Necessary and sufficient criterion for diagonalizability of an endomorphism. Scalar products. Cauchy’s inequality.. Congruent matrices. Symmetric and orthogonal endomorphisms.Spectral theorem. Euclidean geometry. Conics and quadrics.

Textbooks :

M. Abate: Geometria, McGraw-Hill Italia, 1996.
M. Abate, C. de Fabritiis: Esercizi di Geometria, McGraw-Hill Italia, 1999.

Exam :

Written and oral.

Tutorial Session :

Depending on lessons' time table.