LINEAR ALGEBRA AND GEOMETRY
Learning outcomes of the course unit
The course aims to provide basic knowledge and techniques of linear algebra for the purpose of providing tools for resolving linear systems, diagonalising matrices and simply describing the behaviour of geometric bodies in the plane and in space.
Course contents summary
Field of complex numbers: trigonometric and exponential form. Vector and matrix calculus. Determinant and rank of a matrix. Linear systems. Real and complex vector spaces. Bases and dimension. Sum and direct sum of subspaces: Grassmann relation. Linear applications and associated matrices. Eigenvalues and eigenvectors. Diagonalizability of a matrix. Bilinear forms and scalar products. Scalar and Euclidean products. Orthonormal bases. Real symmetrical matrices: diagonalizability. Orthogonal matrices and isometries. Classification of orthogonal matrices of the 2nd and 3rd order. References and coordination in the plane and in space. Parametric and Cartesian representation of straight lines and planes. Parallelism and orthogonality. Distances and angles. Reference changes.
A. Sanini, Lezioni di Geometria, Levrotto&Bella
S. Abeasis, Elementi di Algebra lineare e Geometria, Zanichelli
G. Accascina - V. Villani, Algebra lineare, ETS