Learning objectives
<br />We will study Linear Algebra and its applications, in particular to Geometry in the space.<br />
Course unit content
<br /><br />Linear maps and matrices in the euclidean plane: projections, reflections, rotations, isometries. Group theory. Real and complex vector spaces.<br />Linear maps: kernel and image, the dimension's formula. Basis change and matrices. Matrices of linear maps on finite dimensional vector spaces.<br />Invariant subspaces, eigenvalues, eigenvectors. Diagonalization of operators. Orthogonal matrices and operators. Systems of ordinary differential equations with constant coefficients.<br />Bilinear forms and scalar products. Spectral theorem. Diagonalization of symmetric matrices using orthogonal matrices. Classification of quadric surfaces in the space.
Bibliography
<br />M.Artin, Algebra, Bollati-Boringhieri 1997.