Learning outcomes of the course unit
We shall give to the student the most important tools to:
- solve linear systems
- work with matrices
- solve simple problems about space geometry and eigenvalues.
Course contents summary
1. Linear Geometry in euclidean space. Vectors, length, distance, angle. Lines and planes in the space: description and their positions. Some quadric surfaces.
2. 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.Spanning sets, linearly dependent and independent vectors, bases, dimension.
3. Linear maps and diagonalization. Linear maps and their properties, linear maps and matrices, rotations and reflections in the plane. Eigenvalues, eigenvectors, diagonalization.
L. Alessandrini, L. Nicolodi, Geometria A, Uninova 2002