Università Roma Tre

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.

Flaminio Flamini, Alessandro Verra
Matrici e vettori
Corso di base di geometria e algebra lineare

Edoardo Sernesi:
Geometria 1.

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.

Flaminio Flamini, Alessandro Verra
Matrici e vettori
Corso di base di geometria e algebra lineare

Edoardo Sernesi:
Geometria 1.