Università Roma Tre

1- Linear systems: matrix associated to a linear system; sum of matrices and multiplication by real numbers; reduced matrices; Gauss-Jordan algorithm.
2- Rows by columns product of matrices; invertible matrices; rank of a matrix; Rouche'-Capelli Theorem.
3- Geometrical vectors. Vector spaces. Subspaces. Generating vectors and linearly independent vectors.
4- Basis of a vector space: dimension of a vector space; Grassmann's formula.
5- Linear applications: Kernel and image of a inear application. Dimension of Kernel and Image of a linear application.
6- Matrix associated to a linear application. Diagonalization of linear operators.

F. Flamini; A. Verra: "Matrici e vettori -Corso di base di geometria e algebra lineare" Carocci ed.

1- Linear systems: coefficient matrix; sum of matrices and product for scalars; reduced matricess: Gauss-Jordan algorithm.
2- Product rows for columns of matrices; invertible matrices; rank of a matrix: the Rouche'-Capelli Theorem.
3- Geometric vectors. Vector spaces. Subspaces. Generator vectors and linearly independent vectors.
4- Base of a vector space; dimension; the Grassmann formula.
5- Linear applications: kernel and image of a linear application. The Theorem of nullity plus rank.
6- Matrix associated with a linear application. Diagonalization of linear operators.

Geometria 1, E.Sernesi