Università Roma Tre

Basics of set theory. Vector Spaces.
Linear combinations. Linear dependence and independence. Subspaces. Intesections. Basis and dimension of a vector space.
Matrices. Addition and scalar multiplication. THE VECTOR SPACE OF MXN MATRICES with REAL COEFFICIENTS. Matrix product. DETERMINANT OF A SQUARE MATRIX. PROPERTIES of DETERMINANTs. SARRUS RULE. Laplace Theorem. adjoint and transpose, Diagonal matrices. Elementary operations on rows, echelon reduction. Minors. Rank.
Rouché-Capelli theorem. Cramer Theorem. Linear systems and, homogeneous system associated with a linear system. Compatibility. Gaussian elimination.
Eigenvalues, eigenvectors, eigenspaces. Diagonalization, Scalar and vector product.

R.PROCESI-R.ROTA- LEZIONI DI ALGEBRA LINEARE E GEOMETRIA, ED.ACCADEMICA
R.PROCESI-R.ROTA- ESERCIZI DI GEOMETRIA E ALGEBRA, ED. ZANICHELLI