ALGEBRA AND GEOMETRY
Learning outcomes of the course unit
Linear algebra has links with many branches of mathematics, including abstract algebra, discrete mathematics, calculus, differential equations, geometry, statistics, numerical methods and dynamic systems.
Course contents summary
Algebraic structures: groups, rings, fields: residue classes of a modulo n, integral domain of polynomials with coefficients in a field.
Vector spaces, dependence of vectors, basis, finite or non-finite dimension; subspaces, linear applications, linear forms.
Matrices, determinants, homogeneous and non-homogeneous linear systems; scalar systems: calculus techniques, change-of-basis matrices, matrices associated with linear applications.
Scalar products, Euclidean vector spaces, Eigen values and Eigen vectors; diagonalisable matrices, diagonalisation criteria.
Plane and solid geometry, conic solids.
Some basic notions of computational geometry.
L.A.Lomonaco, Un'introduzione all'algebra lineare, ARACNE editrice
S.Lipschutz-M.Lipson, Algebra Lineare, McGraw-Hill