Elementary set theory.
Introduction to the study of linear systems and vector spaces, with application to the linear Geometry of affine spaces. Linear and Multilinear algebra. Affine spaces and quadratic forms.
Vector spaces and linear systems. Matrix Algebra. Linear Geometry. Affine geometry. Orthogonality. Bilinear and multilinear forms.Inner product. Quadratic forms. Orthogonal transformations.
Linear systems and their resolution. Vector spaces and subspaces. Generators. Linear independence. Basis. The dimension of a vector space. Rank of matrices. Matrix Algebra. Determinants. Linear maps and their matrices. Endomorphisms. Diagonalization. Linear Geometry in dimension 2 and 3. Affine geometry. Standard inner product. Orthogonality. Bilinear and multilinear forms. Orthogonal basis. Symmetric forms and diagonalization. Geometric transformations. Real quadratic forms.
C.Ciliberto, Algebra Lineare, Boringhieri.
E. Sernesi, Geometria 1, Boringhieri.
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Lectures and class exercises.
Written and oral tests. The written test is based on the solution of exercises. The oral test will examine the theoretical basis which determine the methods for the solution of problems.
The web page of the teacher contains downloadable files on some topics of the course.