Programme

Relations, equivalence relations and order relations. Partitions and quotient set. Functions and composition of functions. Injections, surjections, bijections and inverse function. Algebraic structures: groups and fields. Linear system. Gauss elimination. Matrices and matrix operations. Determinant, rank and inverse matrix. Rouché-Capelli theorem and Cramer theorem. Vector spaces and subspaces. Numeric vectors and geometric vectors. Linear independence, basis and dimension of a vector space. Inner product and vector product. Affine spaces. Euclidean geometry of R^2 and R^3. Lines, planes, sphere, projections and symmetries. Linear function and endomorphisms. Kernel and image of a linear function and rank-nullity theorem. Eigenvalues and eigenvectors. Diagonalization. Classification of conics.

Core Documentation

F.J. Leon Trujillo, P. Mercuri. Elementi di Algebra Lineare, Ed. Efesto
F.J. Leon Trujillo, P. Mercuri. Elementi di Geometria Affine ed Euclidea, Ed. Efesto

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Programme

Vector spaces. Linear dependence and independence of vectors. Basis. Dimension. Subspaces. Subspace sum. Subspace intersection. Grassmann’s relation. Matrices. Determinants. Inverse matrix. Reduction of a matrix into treads. The rank of a matrix. Linear systems. Theorem of Rouche-Capelli. Cramer's theorem. Method of Gaussian elimination. Linear applications. Kernel. Image. Linear maps and linear dependence. Linear maps and matrices. Change of basis. Similar matrices. Diagonalization of an endomorphism. Eigenvalues. Eigenvectors. Eigenspaces. Characteristic polynomial. Scalar products. Euclidean vector spaces. Elements of affine and Euclidean geometry of the plane and space.

Core Documentation

F.J. Leon Trujillo, P. Mercuri. Elementi di Algebra Lineare, Ed. Efesto.
F.J. Leon Trujillo, P. Mercuri. Elementi di Geometria Affine ed Euclidea, Ed. Efesto.

Reference Bibliography

M. Abate. Geometria.

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