Università Roma Tre

1- Linear Systems: coefficients matrix, sum and scalar multiples of matrices; reduced form and echelon reduced form; Gauss-Jordan Algorithm.
2- Matrix product; invertible matrices; rank of a matrix; Rouche'-Capelli Theorem.
3- Vectors and Vector spaces. Subspaces; linear indipendence and generators.
4- Basis of a vector space; dimension; Grassmann Formula.
5- Linear maps; kernel and image of a linear map. Rank-nullity Theorem. Matrix associated to a linear map.
6- Eigenvalues and Eigenvectors. Diagonalization of linear maps.

F. Flamini, A. Verra: Matrici e vettori. Corso di base di geometria e algebra lineare. Carocci.