In the course students are taught the basics of linear algebra and analytic geometry in the plane and in space. In particular the essential notions for solving a system of linear equations are developed, to calculate the rank of a matrix and of its other invariants. As far as the notions of analytical geometry are
concerned, particular attention will be paid to the notion of scalar product and to the study of conics and quadrics
concerned, particular attention will be paid to the notion of scalar product and to the study of conics and quadrics
teacher profile teaching materials
- Square matrices and determinants Definition of determinant, properties of determinants, calculation of a determinant, determinants and invertible matrices, - Vector spaces
- Geometric vectors, definition and examples of vector spaces, linear independence of vectors, finite dimensional vector spaces, bases. And basic change
- Scalar products and Euclidean spaces, Geometric scalar product, Scalar products, perpendicularity and orthogonal bases, orthonormal bases and orthogonal matrices, Cartesian coordinates on a Euclidean space, fundamental metric properties, isometries of the Euclidean plane
- Geometry in the plane and in the space Points and straight lines in the plane, angle between two straight lines, formulas of flat geometry, bundles of straight lines, circumferences, straight points and planes in space, equations of straight lines, planes, spheres, circumferences.
- Linear applications Core and image of a linear application, linear applications and matrices, linear operators, eigenvalues and eigenvectors of a linear operator, characteristic polynomial, search for eigenvalues and eigenvectors -Conic and conic quadrics and their metric properties, canonical forms of conics, reduction to canonical form of conics, quadrics, euclidean canonical forms of quadrics Recommended texts: further information will be given at the beginning of the course.
Matrici e vettori
Corso di base di geometria e algebra lineare
Edoardo Sernesi:
Geometria 1.
Programme
Systems of linear equations and matrices reduction by rows of a matrix, resolution of systems of linear equations, product of matrices, rank of a matrix, invertible matrices and their construction, Rouchè Capelli's theorem- Square matrices and determinants Definition of determinant, properties of determinants, calculation of a determinant, determinants and invertible matrices, - Vector spaces
- Geometric vectors, definition and examples of vector spaces, linear independence of vectors, finite dimensional vector spaces, bases. And basic change
- Scalar products and Euclidean spaces, Geometric scalar product, Scalar products, perpendicularity and orthogonal bases, orthonormal bases and orthogonal matrices, Cartesian coordinates on a Euclidean space, fundamental metric properties, isometries of the Euclidean plane
- Geometry in the plane and in the space Points and straight lines in the plane, angle between two straight lines, formulas of flat geometry, bundles of straight lines, circumferences, straight points and planes in space, equations of straight lines, planes, spheres, circumferences.
- Linear applications Core and image of a linear application, linear applications and matrices, linear operators, eigenvalues and eigenvectors of a linear operator, characteristic polynomial, search for eigenvalues and eigenvectors -Conic and conic quadrics and their metric properties, canonical forms of conics, reduction to canonical form of conics, quadrics, euclidean canonical forms of quadrics Recommended texts: further information will be given at the beginning of the course.
Core Documentation
Flaminio Flamini, Alessandro VerraMatrici e vettori
Corso di base di geometria e algebra lineare
Edoardo Sernesi:
Geometria 1.
Type of delivery of the course
The lessons are held in the traditional way, in presence and in the classroom; in case of extension of the provisions for the COVID-19 emergency, the lessons will take place remotely through the use of the University Teams platformType of evaluation
Written exam, Oral exam; partial written tests during the course. teacher profile teaching materials
Programme
see profile of the teacher holding the courseCore Documentation
see profile of the teacher holding the courseType of delivery of the course
see profile of the teacher holding the courseType of evaluation
see profile of the teacher holding the course