Università Roma Tre

Vector spaces and subspaces. Matrices. Row by column multiplication. Gaussian elimination and homogenous linear systems. Generators of a vector space end linearly independent vectors. Basis and dimension of a vector space. Grassmann Formula. Rank of a matrix and invertible matrices. Rouché-Capelli Theorem and solutions of a linear system. Determinant. Linear maps. Kernel and image of a linear map. The nullity plus rank theorem. Matrix associated to a linear map. Change of basis. Dual vector space and transpose of a linear map. diagonalization of linear operators. Minimal polynomial. Jordan canonical form.

Marco Manetti, Algebra lineare, per matematici.
Serge Lang, Algebra Lineare, Bollati Boringhieri.
Edoardo Sernesi, Geometria I, Bollati Boringhieri.