Università Roma Tre

Systems of linear equations. Coefficient matrix. Matrix addition and scalar multiplication. Gauss-Jordan elimination. Row by Column multiplication. Determinant. Invertible matrices. Rank of a matrix and Rouche'-Capelli Theorem. Geometric vectors. Vector spaces and subspaces. Generators and linearly independent vectors. Basis and dimension. Linear maps. Kernel and image of a linear map. Rank plus nullity Theorem. Matrix associated with a linear map. Diagonalization of linear maps.

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

Linear Algebra:
Matrices. Determinants. Rank. Linear systems. Vector spaces. Linear applications. Eigenvalues ​​and eigenvectors.
Diagonalization. Scalar product. Symmetric operators. Spectral theorem.
Geometry:
Affine geometry of the plane and space. Euclidean geometry of the plane and space.

F. Flamini, A. Verra: Matrici e vettori. Corso di base di geometria e algebra lineare. Carocci.
Also suggested:
E. Schlesinger: Algebra lineare e geometria, Zanichelli.
L. Mauri e E. Schlesinger: Esercizi di algebra lineare e geometria, Zanichelli.