GEOMETRIA A - L

Basic knowledge of linear algebra and geometry

The course is structured in participatory lectures and cooperatives that provide for ongoing checks. It will aim to ensure consistency between the training objectives and the methods used, combining the frontal methodology with the dialogue one but including the possibility of applying knowledge through exercises .

Should the circumstances require online or blended teaching, appropiate modifications to what is hereby stated may be introduced in order to achieve the main objectives of the course

Geometric vectors in the plane and space- Vector spaces, subspaces and operations with them-Matrices, determinants and linear systems and their properties- Linear fuctions and their properties – Eigenvalues and eigenvectors of an endomorphisms- Diagonalization of an endomorphism- Bilinear forms, real scalar products- Symmetrical endomorphisms – Spectral theorem and its corollaries-

Linear geometry in the plane and space - Conic, invariants orthogonal- classification affine of conic non-degenerate-polarity- Quadrics degenerate and non- degenerate - Cones and cylinders- Classification affine of quadrics non degenerate-Tangent lines and tangent planes for a quadric- Plane sections of irreducible quadrics.

Lezioni di Algebra lineare e Geometria Greco-Valabrega.