Learning outcomes of the course unit
We will study Linear Algebra and its applications, in particular to Geometry in the space.
Course contents summary
Linear Geometry in euclidean space. Vectors, length, distance, angle. Lines and planes in the space: description and their positions. Some quadric surfaces.
Vectors, matrices, linear systems. Vectors of the n-dimensional euclidean space and their operations. Scalar product, angle, orthogonality. Matrices: operations and properties. Determinants. Linear systems theory, the Gauss algorithm, the rank of a matrix. Rouché-Capelli Theorem.
Real and complex vector spaces.
Linear maps: kernel and image, the dimension's formula. Basis change and matrices. Matrices of linear maps on finite dimensional vector spaces.
Invariant subspaces, eigenvalues, eigenvectors. Diagonalization of operators. Orthogonal matrices and operators. Systems of ordinary differential equations with constant coefficients.
Bilinear forms and scalar products. Spectral theorem.
L. ALESSANDRINI, L. NICOLODI, GEOMETRIA A, ed. UNINOVA (PR)
L. ALESSANDRINI, GEOMETRIA B, ed. UNINOVA (PR)
JOINT WRITTEN ORAL EXAM.
Assessment methods and criteria
written and oral examination