Linear systems and matrices. Vectorial spaces. Symmetric matrices and spectral theorem. Orthogonality. Quadratic forms. Lines, planes and hyperplanes in R^n.
Notes written by the teacher and/or
Marco Abate, Algebra lineare, McGraw-Hill.
Learning Objectives
to get acquainted with real linear algebra with elements of geometry
Prerequisites
nothing
Teaching Methods
lessons and interactive lessons.
Further information
The course has a moodle page on e-l. unifi
Type of Assessment
Intermediate exams.
Written and oral exams.
Course program
Sets. Functions and operations. Linear systems and Gauss algorithm. Martices. Homogeneous and not homogeneous systems. Linear independence and basis. Dimension of a vectorial space. Subspaces. Subspace generated by a set of vectors. Square, triangular, diagonal and symmetric matrices. Transpose of a matrix. Rank of a matrix. Scalar product of two vectors. Angle between two vectors. The geometric universe R^n.Parametric equation of a line. Equation of a hyperplane. Norm of a vector. Cauchy-Schwarz inequality. Parallelism and orthogonality. Parallel and othogonal lines and planes. Linear applications and matrices. Kernel and image of a linear application. Determinant. Rank of a matrix through its minors.Inverse of a matrix and its computation by Gauss algorithm and by minors. Eigenvalues and eigenvectors. Spectral theorem. Quadratic forms. Basics on conics and quadrics. The ellipsoid case.