
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.
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 :
room 58, Mathematical Sciences Department,hours
according to the lecture timetable
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